Concept of “Problem based on ages”–07

Question: The ratio of present ages of P and Q is 7: 3. After 4 years their ages will be in the ratio of 2: 1. What is the present age of P? [Ans. (b) 28 yrs]

(a) 24 yrs (b) 28 yrs (c) 32 yrs (d) Data inadequate (e) none of these

Solution:

Detailed Explanation:

First Method: Let the present ages of P and Q are 7x and 3x. After 4 years their ages will be 7x+4 and 3x+4. Given that the ratio of their ages after 4 years is 2: 1.

(7x + 4)/(3x + 4) = 2: 1

Or, x = 4 years

P = 7×4 = 28 yrs Ans.

Second Method: Let the ages of P and Q after 4 years is 2x: 1x. Their present ages are respectively 2x-4 and 1x-4. Given that the ratio of their present ages is 7: 3.

(2x - 4)/(1x - 4) = 7: 3

Or, x = 4 ×4 = 16 years

P = 2×16 - 4 = 28 yrs Ans.

Concept of “Problem based on ages”–06

Question: If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68. If the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P. [Q की उम्र के दो गुणे में, P और R की उम्र को जोड़ने पर 59 मिलता है. P की उम्र के तीन गुणे में Q और R की उम्र को जोड़ने पर 68 मिलता है, जबकि P की उम्र को Q के तीन गुणे तथा R के तीन गुणे में जोड़ने पर यह 108 होता है. P  की उम्र क्या है?]  [Ans. (d) 12 years]                                                                     

(a) 15 yrs   (b) 19 yrs   (c) 17 yrs   (d) 12 yrs (e) none of these

Detailed Explanation: Let the “P”, “Q” and “R” are the ages of P, Q and R respectively.  Given that                          

                               P +  2Q +  R = 59     ---------------  (1)

                             3P +    Q +  R = 68     ---------------  (2)

                               P +  3Q +3R = 108   ---------------  (3)

To get the age of P, here, just two equations – (2) and (3) are sufficient. When we multiply equation (2) by 3, and subtract equation (3) from it, we get

                             9P +  3Q + 3R = 204     --------------- (2)

                               P +  3Q + 3R = 108     --------------- (3)

                             -     -        -          -

                     --------------------------------------------------------

                             8P                   =   96

                                   P  = 12 years Ans.

2. PROBLEMS BASED ON AGES: 2nd part

2. PROBLEMS BASED ON AGES: 2^nd part

7. (i) Ratio of Ashok’s age to Pradeep’s age is equal to 4 : 3. Ashok will be 26 years old after 6 years. How old is Pradeep now? (v'kksd vkSj iznhi dh mez dk vuqikr 4 % 3 gSA 6 lky ckn v'kksd dh mez 26 lky gks tk;sxhA iznhi dh orZeku mez D;k gS\)         

(a) 15 yrs      (b) 19.5 yrs     (c) 21 yrs     (d) 12 yrs   (e) none

(ii) Sachin was twice as old as Ajay 10 years back. How old is Ajay today if Sachin will be 40 years old 10 years hence? (10 lky igys lfpu dh mez vt; dh nks xq.kh FkhA vt; dh oÙkZeku mez D;k gS] ;fn 10 o’kZ ckn lfpu dh mez 40 o’kZ gks tk;s\)   

(a) 20 yrs   (b) 10 yrs   (c) 30 yrs   (d) 15 yrs   (e) none of these

(iii) The ratio of Vimal  and Arun’s ages is 3 : 5 and sum of their ages is 80 years. The ratio of their ages after 10 years will be : (foey vkSj v:.k dh mez dk vuqikr 3 % 5 gS vkSj mudh mez dk ;ksxQy 80 lky gSA 10 lky ckn mudh mez dk vuqikr Kkr djsaA)        

(a) 2 : 3     (b) 1 : 2        (c) 3 : 2      (d) 3 : 5    (e) none of these

(iv) In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is (10 lky ckn A dh mez] 10 lky igys dh B dh mez dh nks xq.kh gksxhA ;fn vHkh A, B ls 9 lky cM+k gS] rks B dh oÙkZeku dk mez D;k gS\) :   

(a) 29 yrs      (b) 39 yrs   (c) 19 yrs   (d) 49   (e) none of these

(v) Jayesh is twice as old as Vijay and half as old as Suresh. If the sum of Suresh’s and Vijay’s ages is 85 years, what is Jayesh’s age in years? (t;s'k dh mez fot; dh nks xq.kh gS] tcfd lqjs'k dk vk/kh gSA ;fn lqjs'k vkSj fot; dh mez dk ;ksxQy 85 lky gks] rks t;s'k dh mez D;k gS\)  

(a) 36 yrs   (b) 34 yrs  (c) 38 yrs (d) Data inadequate  (e) none

(vi) Present age of Rahul is 8 years less than Ritu’s present age. If 3 years ago Ritu’s age was ‘x’, which of the following represents Rahul’s present age? (jkgqy dh oÙkZeku mez fjrq dh oÙkZeku mez ls 8 lky de gSA ;fn 3 lky igys fjrq dh mez X o’kZ Fkh] rks jkgqy dh orZeku mez D;k gS\)    

(a)  x+3      (b)  x-5      (c) x-3+8   (d) x+3+8   (e) none of these

(vii) If 6 years are subtracted from the present age of Randheer and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Mahesh whose age is 5 years, then what is the age of Randheer ? (;fn j.k/khj dh mez ls 6 ?kVk fn;k tk;s rFkk 'ks"k dks 18 ls Hkkx fn;k tk;s] rks mlds iksrs vuwi dh mez izkIr gksrh gSA ;fn vuwi] egs'k ls 2 lky NksVk gS] tks ¼egs'k½ 5 lky dk gS] rks j.k/khj dh mez D;k gS\)  

(a) 96 yrs  (b) 84 yrs   (c) 48 yrs (d) 60 yrs    (e) none of these

(viii) The sum of the ages of a father and son is 45 yrs. 5 yrs ago; the product of their ages was 4 times the father’s age at that time. The present age of the father is (firk vkSj iq= dh mez dk ;ksxQy 45 o"kZ gSA 5 o"kZ igys mu nksuksa dh mez dk xq.kuQy] ml le; dh mlds firk dh mez dk pkj xq.kk Fkk( rks firk dh oÙkZeku mez D;k gS\):

(a) 39 yrs (b) 36 yrs (c) 40 yrs   (d) Data inadequate   (e) none

8. (i) If the product of the present ages of a father and his son is 900 years and the ratio of their present ages is 25 : 9. Find their present ages. (firk vkSj iq= dh mez dk xq.kuQy 900 o"kZ gSA ;fn mudh mez dk vuqikr 25 % 9 gks( rks mudh oÙkZeku mez Kkr djsaA)                                              

(a) 45yrs,20yrs  (b) 42yrs, 8yrs (c) 50yrs, 18yrs (d) 41yrs, 9yrs           

(ii) If the product of the present ages of the father and his son is 3600 years and the ratio of their present ages is 16 : 9. Find the difference of their present ages. (firk vkSj iq= dh mez dk xq.kuQy 3600 o"kZ gSA ;fn mudh mez dk vuqikr 16 % 9 gks( rks nksuksa dh mez dk varj Kkr djsaA)         

(a) 40 yrs  (b) 53 yrs  (c) 45 yrs  (d) 35 yrs   (e) none of these

9. (i) A man’s age is 125% of what it was 10 years ago, but 83%  of what it will be after 10 years. What is his present age? (,d vkneh dh orZeku mez mlds 10 lky igys dh mez dk 125% gS] tcfd ;g 10 lky ckn dh mldh mez dk 83% gS( rks mldk oÙkZeku mez D;k gS\)                                                    

(a) 40 yrs  (b) 55 yrs   (c) 45 yrs     (d) 50 yrs  (e) none of these

(ii) A man’s age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is his present age? (,d vkneh dh mez mlds 10 lky igys dh mez dk  gS] tcfd ;g 10 lky ckn ds mldh mez dk  gS( rks mldh oÙkZeku mez D;k gS\)                                       

(a) 25 yrs    (b) 30 yrs    (c) 35 yrs   (d) 40 yrs   (e) none of these

(iii) A man’s age is 133 % of what it was 10 years ago, but 80% of what it will be after 10 years. What is his present age? (,d vkneh dh mez mlds 10 lky igys dh mez dk 133 % gS] tcfd ;g 10 lky ckn ds mldh mez dk %  gS( rks mldh oÙkZeku mez D;k gS\)                                        

(a) 25 yrs  (b) 45 yrs  (c) 40 yrs (d) 50 yrs     (e) none of these

(iv) 20 years ago my age was 1/3 of what it is now. What is my present’s age? (20 lky igys esjh mez] esjh orZeku mez dk   Fkh] rks esjh oÙkZeku mez D;k gS\)                                        

(a) 20 yrs  (b) 10 yrs    (c) 30 yrs   (d) 40 yrs   (e) none of these

(v) Kamla got married 6 years ago. Today her age is 1 times her age at the time of marriage. Her son’s age is  ^th of her age. What is the age of her son ? (deyk dh 'kknh 6 lky igys gqbZA vkt mldh mez] mldh 'kknh ds le; dh mez dk 1 xq.kh gSAmlds csVs dh mez] mldh orZeku mez dk  xq.kh gS] rks mlds csVs dh oÙkZeku mez D;k gS\) :   

(a) 2 yrs    (b) 4 yrs   (c) 3 yrs      (d) 5 yrs     (e) none of these

10. (i) The product of the ages of Harish and Seema is 240. If twice of the age of Seema is more than Harish’s age by 4 years, what is Seema’s age in years?  (gjh'k vkSj lhek dh mez dk xq.kuQy 240 gSA ;fn lhek dh mez dk nks xq.kk gjh'k dh mez ls 4 lky T;knk gks] rks lhek dh mez crk,WaaA)                                  

(a) 12 yrs (b) 10 yrs  (c) 20 yrs(d) 14 yrs  (e) Data inadequate

(ii) In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years age, which is 48. What is the total number of students in the school? (fdlh Ldwy esa 20% Nk= 8 lky ls de ds gSaA 8 o’kZ ls cM+h mez ds Nk=ksa dh la[;k] Bhd 8 o’kZ dh mez ds Nk=ksa dh la[;k dk  gks] tks fd 48 gS] rks Ldwy esa Nk=ksa dh dqy la[;k crk,WaA)   

(a)  72       (b) 120      (c) 80       (d) 150       (e) none of these

(iii) If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68. If the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P(Q dh mez ds nks xq.ks esa] P vkSj R dh mez dks tksM+us ij 59 feyrk gSA P dh mez ds rhu xq.ks esa] Q vkSj R dh mez dks tksM+us ij 68 feyrk gS] tcfd P dh mez dks Q ds rhu xq.ks rFkk R ds rhu xq.ks esa tksM+us ij ;g 108 gksrk gSA P dh mez D;k gS\)                                                                           

(a) 15 yrs   (b) 19 yrs   (c) 17 yrs   (d) 12 yrs  (e) none of these

11. (i) The ratio of A’s and B’s ages is 4 : 5. If the difference between the present age of B and the age of A 5 years hence is 3, then what is the total of present ages of A and B ? (A vkSj B dh mez dk vuqikr 4 % 5 gSA ;fn 5 lky ckn dh B dh mez vkSj A dh orZeku mez dk varj 3 o’kZ gks] rks A vkSj B dh mez dk dqy ;ksx Kkr djsaA)                 

(a) 27 yrs  (b) 62 yrs   (c) 72 yrs   (d) data inadequate (e) none  

(ii) The ratio of P’s and Q’s ages is 5 : 7. If the difference between the present age of Q and the age of P 6 years hence is 2, then what is the total of present ages of P and Q? (P vkSj Q dh mez dk vuqikr 5 % 7 gSA ;fn Q dh orZeku mez vkSj P dh 6 lky ckn dh mez dk varj 2 o’kZ gks] rks P vkSj Q dh mez dk dqy ;ksx Kkr djsaA)                   

(a) 48 yrs (b) 52 yrs  (c) 56 yrs (d) data inadequate   (e) none  

Concept of “Problem based on ages”–05

Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years age, which is 48. What is the total number of students in the school? [एक स्कूल में 20% विद्यार्थी 8 वर्ष से कम उम्र के हैं. 8 वर्ष से ज्यादा उम्र के विद्यार्थियों की संख्या, 8 वर्ष की उम्र के विद्यार्थियों की संख्या, जो कि 48 है, के 2/3 के बराबर है.स्कूल में विद्यार्थियों की कुल संख्या क्या है?] [Ans. (e) none of these (100)]  

(a)  72       (b) 120      (c) 80       (d) 150       (e) none of these

Solution:

Detailed Explanation: Given that in a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years age, which are 48.

Percentage of the number of students of 8 years of age and above 8 years of age = 100% - 20% = 80%

Since the number of students of above of 8 years of age is 2/3^rd of the number of students of 8 years of age, so their ratio is 2:3 It is also given that the number of students of 8 years of age is 48

            8 years of age ≡ 3 ≡ 48

Above 8 years of age ≡ 2

                           Sum ≡ 5 ≡? = 80

Also, 80% ≡ 80

So, 100% ≡? = 100 Ans.

Concept of “Problem based on ages”–04

Question: Present ages of P and Q are in the ratio 5 : 6 respectively. Seven years hence this ratio becomes 6 : 7 respectively. What is P’s present age in years? [वर्तमान में P तथा Q की उम्र का अनुपात क्रमशः 5 : 6 है; जवकि 7 वर्ष के वाद यह 6  :7 हो जायेगा. P की वर्तमान उम्र क्या है?] [Ans. (a) 35 years] 

(a)  35     (b) 42    (c) 49   (d) can’t be determined (e) None of these 

Solution:

Detailed Explanation:

Concept: When the differences between the terms of the ratios are the same, then this difference can be taken as equivalent to the real difference.

First Method: Given that the present ages of P and Q are in the ratio 5 : 6 respectively; whereas after seven years, this ratio will become 6 : 7 respectively. Here the difference between the corresponding terms is the same.  i. e., 6 – 5 = 7 – 6 = 1 ≡ 7 years (Real difference between the ages of  “present” and “seven year hence” is 7)

         Difference = 1 ≡ 7 years

Present age of P = 5 ≡ 35 years Ans.

Second Method: Let the ages of P and Q, at present, are 5x and 6x. So, their ages, after seven year will be 5x +7 and 6x + 7. But this ratio is given as 6: 7

So, (5x +7)/( 6x + 7) = 6/7

Or, (36–35) x = 7× (7- 6)

Or, x = 7

So, the present age of P = 5x =5×7 = 35 years  

==============================================================================================================================================

PROBLEMS BASED ON AGES–03

Question: The sum of the ages of a mother and her daughter is 50 years. Also, 5 years ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter? [एक माता और उसकी पुत्री की उम्रों का योगफल 50 वर्ष है. 5 वर्ष पहले माता की आयु पुत्री की आयु की 7 गुणी थी. बताएं कि आज माता और पुत्री की आयु क्या है?]  [Ans. (c) 40 yrs, 10 yrs]                                     

(a) 45 yrs, 5 yrs   (b) 42 yrs, 8 yrs  (c) 40 yrs, 10 yrs (d) 41 yrs, 9 yrs (e) none of these          

Solution:

Detailed Explanation:

Concept: When the sum of the ages of two persons goes to 5 years ago, it is reduced by 10 years (as the age of each of the persons is reduced by 5 years)

First Method: Given that the sum of the ages of a mother and her daughter is 50 years (at present), so the sum of their ages 5 years ago was 50-10 = 40 years.

Also given that the ratio of the ages of the mother and her daughter 5 years ago was 7:1, so that the sum is 8 (in terms of ratio). 

8 ≡ 40 years

1 ≡? = 5 years (the age of daughter 5 years ago)

7 ≡? = 35 years (the age of mother 5 years ago)

Therefore, the present age of mother is 35+5 = 40 years and the present age of daughter is 5+5 = 10 years. Ans.

Second Method: Let the ages of daughter and mother 5 years ago were “x” years and “7x” years.  So, their present ages are respectively (x+5) years and (7x+5) years.

Given that the sum of the present ages of mother and her daughter is 50 years, so

(7x+5) + (x + 5) = 50 or, 8x = 40 or, x = 5

Therefore, the present age of mother = 7×5+5 = 40 yrs and the present age of daughter = 5+5 = 10 yrs Ans.   

PROBLEMS BASED ON AGES – 02

Question: A man’s age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is his present age? [एक व्यक्ति की उम्र उसके 10 वर्ष पहले की उम्र का 150% है; जबकि 10 वर्ष बाद की उसकी उम्र का यह 75% होता है. तो, उसकी वर्तमान उम्र क्या है?] [Ans. (b) 30 years]                                                                                                                         

(a) 25 yrs    (b) 30 yrs    (c) 35 yrs   (d) 40 yrs   (e) none of these

Detailed Explanation:

First Method: If the age of the man, 10 years ago is taken as 100%, then his present age becomes 150%. Obviously,  difference between the ages at these two stages is (150-100)% = 50%, but the difference is 10 years.

So, if 50% is equivalent to 10 years, then 150% (present age) should be definitely 30 years. Ans.  

    Difference = 50% ≡ 10 years

Present age = 150% ≡? = 30 years Ans.

Second Method: If the age of the man, 10 years hence is taken as 100%, then his present age becomes 75%. Obviously,  difference between the ages at these two stages is (100-75)% = 25%, but the difference is 10 years.

So, if 25% is equivalent to 10 years, then 75% (present age) should be definitely 30 years. Ans.  

  Difference = 25% ≡ 10 years

Present age = 75% ≡? = 30 years Ans.

PROBLEMS BASED ON AGES (आयु आधारित प्रश्न) - 1st part

1.(i) The age of the father 3 years ago was 7 times the age of his son. At present the father’s age is five times that of his son. What are the present ages of the father and the son? (3 o"kZ igys firk dh meziq= dh mez dh 7 xq.kh FkhA oÙkZeku esa firk dh mez iq= dh mez dh 5 xq.kh gS( rks oÙkZeku esa firk vkSj iq= dh mez Kkr djsa\)

(a) 45yrs, 9yrs (b) 40yrs, 9yrs (c) 42yrs, 8yrs (d) 35yrs, 9yrs  

(ii) The age of Arvind’s father is 4 times his age. If 5 years ago, father’s age was 7 times of the age of his son at that time, what is Arvind’s father’s present age ?  (vjfoUn ds firk dh mez mldh mez dh 4 xq.kh gSA ;fn 5 lky igys mlds firk dh mez mldh mez dh 7 xq.kh Fkh( rks oÙkZeku esa mlds firk dh mez D;k gS\) 

(a) 35 yrs    (b) 40 yrs    (c) 42 yrs   (d) 30 yrs     (e) none

(iii) 6 years ago Jagunnath was twice as old as Badri. If the ratio of their present ages is 9 : 5 respectively, what is the difference between their present ages in years ? (6 lky igys txUukFk dh mez] cnjh ds mez dh nks xq.kh FkhA ;fn oÙkZeku esa mudh mez dk vuqikr 9 % 5 gks( rks oÙkZeku esa mudh mez esa D;k varj gSA)      

(a) 30 yrs  (b) 35 yrs (c)can’t be determined (d) 24 yrs                    

(iv) 10 yrs ago A was half of B in age. If the ratio of their present ages is 3:4, what will be the total of their present ages? (10 lky igys A dh mez B dh vk/kh FkhA ;fn mudh oÙkZeku mez dk vuqikr 3 % 4 gS( rks mudh oÙkZeku mez dk dqy ;ksx fdruk gS\)                                                           

(a) 35 yrs  (b) 40 yrs  (c) 42 yrs   (d) 30 yrs   (e) none of these

2.(i) At present the age of the father is five times that of the age of his son. Three years hence, the father’s age would be four times that of his son. Find the present ages of the father and the son. (oÙkZeku esa firk dh mez iq= ds mez dh 5 xq.kh gSA rhu lky ckn firk dh mez iq= ds mez dh pkj xquk gks tk;sxh( rks oÙkZeku esa nksuksa dh mez Kkr djsaA)                                             

(a) 45yrs, 9yrs  (b) 40yrs, 9yrs  (c) 42yrs, 8yrs (d) 35yrs, 9yrs           

(ii) The ratio between the present ages of P and Q is 5 : 8. After 4 years, the ratio between their ages will be 2 : 3. What is Q’s age at present? (P vkSj Q dh mez dk oÙkZeku vuqikr 5 % 8 gSA pkj lky ckn mudh mez dk vuqikr 2 % 3 gks tk,xkA oÙkZeku esa Q dh mez D;k gS\)                                              

(a) 35 yrs     (b) 32 yrs     (c) 24 yrs   (d) 30 yrs     (e) none

(iii) The age of Mr. Ramesh is four times the age of his son. After ten years the age of Mr Ramesh will be only twice the age of his son. Find the present age of Mr Ramesh’s son. (jes'k dh mez mlds iq= dh mez dh pkj xq.kh gSA 10 lky ds ckn jes'k dh mez vius iq= dh mez dh dsoy nks xq.kh gksxhA oÙkZeku esa jes'k ds iq= dh mez D;k gS\)           

(a) 10 yrs  (b) 5 yrs   (c) 11 yrs  (d) 15 yrs   (e) none of these

(iv) The ratio of present ages of P and Q is 7 : 3. After 4 years their ages will be in the ratio of 2: 1. What is the present age of P? (oÙkZeku esa P vkSj Q dh mez dk vuqikr 7 % 3 gSA 4 lky ds ckn mudh mez dk vuqikr 2 % 1 gksxkA P dh oÙkZeku mez D;k gS\)                                  

(a) 24 yrs  (b) 28 yrs   (c) 32 yrs   (d) Data inadequate (e) none

(v) The ratio of the ages of father and son at present is 6 : 1. After 5 years, the ratio will become 7 : 2. The present age of son is : (oÙkZeku esa firk vkSj iq= dh mez dk vuqikr 6 % 1 gSA 5 lky ds ckn ;g vuqikr 7 % 2 gksxk( rks oÙkZeku esa iq= dh mez D;k gSA)  

(a) 10 yrs    (b) 6 yrs      (c) 5 yrs        (d) 9 yrs     (e) none

(vi) Present ages of P and Q are in the ratio 5 : 6 respectively. Seven years hence this ratio becomes 6 : 7 respectively. What is P’s present age in years? (oÙkZeku esa P vkSj Q dh mez dk vuqikr Øe'k% 5 % 6 gS( tcfd 7 lky ckn ;g 6 % 7 gks tk,xk( rks oÙkZeku esa P dh mez D;k gSA)                                                         

(a)  35     (b) 42       (c)  49   (d)can’t be determined (e)  none   

3. (i) Three years earlier the father was 7 times as old as his son. Three years hence the father’s age would be four times that of his son. What are the present ages of the father and the son? (vkt ls rhu lky igys ,d firk dh mez iq= dh mez dh 7 xq.kh FkhA rhu lky ckn firk dk mez iq= dh pkj xq.kh gks tk;sxh( rks oÙkZeku esa nksuksa dh mez Kkr djsaA)           

(a) 45yrs, 9yrs (b) 40yrs, 9yrs (c) 42yrs, 8yrs(d) 35yrs, 9yrs            

(ii) One year ago the ratio between Samir’s and Ashok’s age was 4: 3. One year hence the ratio of their ages will be 5 : 4. What is the sum of their present ages in years? (,d lky igys lehj vkSj v'kksd ds mez dk vuqikr 4 % 3 FkkA ,d lky ckn muds mez dk vuqikr 5 % 4 gks tkrk gSA oÙkZeku esa nksuksa ds mez dk ;ksx Kkr djsaA)   

(a) 15 yrs  (b) 13 yrs  (c) 20 yrs  (d) 16 yrs   (e) none of these

(iii) 10 years ago Chandravati’s mother was 4 times older than her daughter. After 10 years, the mother will be twice older than the daughter. What is the present age of Chandravati? (10 lky igys pUnzkorh dh ek¡ vius csVh ls pkj xq.kk cM+h FkhA 10 lky ckn ek¡ dh mez csVh ls nks xq.kh gks tk,xh( rks pUnzkorh dh oÙkZeku mez D;k gS\)                                                                                 

(a) 5 yrs   (b) 10 yrs    (c) 20 yrs  (d) 30 yr   (e) none of these

4. (i) The sum of the ages of a mother and her daughter is 50 years. Also, 5 years ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter ? (ek¡ vkSj csVh dh mez dk ;ksxQy 50 o"kZ gSA 5 lky igys ek¡ dh mez csVh dh mez dk 7 xq.kk Fkh( rks oÙkZeku esa ek¡ vkSj csVh dh mez D;k gSa\)                                      

(a) 45yrs, 5yrs   (b) 42yrs, 8yrs (c) 40yrs, 10yrs (d) 41yrs, 9yrs           

(ii) The sum of the ages of Sweta and her mother is 63 years. Also, 4 years ago, the mother’s age was 4 times of Sweta’s age at that time. What is the present age of Sweta’s mother? ('osrk vkSj mldh ek¡ dh mez dk ;ksxQy 63 lky gSA 4 lky igys ek¡ dh mez 'osrk dh mez dh 4 xq.kk FkhA oÙkZeku esa 'osrk dh ek¡ dh mez D;k gS\)                               

(a) 40 yrs   (b) 53 yrs  (c) 45 yrs  (d) 48 yrs   (e) none of these

5.(i) The sum of the ages of a son and father is 56 years. After 4 years, the age of the father will be three times that of the son. What is the age of the son? (firk vkSj iq= dh mez dk ;ksxQy 56 lky gSA 4 lky ckn firk dh mez iq= dh mez dh rhu xq.kh gks tk;sxh( rks iq= dh mez D;k gS\)                                                 

(a) 8 yrs    (b) 10 yrs   (c) 12 yrs   (d) 15 yrs  (e) none of these

(ii) The sum of the ages of the father and his daughter is 66 years. After 3 years, the age of the father will be three times that of his daughter. What is the ratio of the present ages of the father and his son? (firk vkSj iq=h dh mez dk ;ksxQy 66 lky gSA rhu lky ckn firk dh mez iq=h dh mez dh rhu xq.kh gks tk,xhA oÙkZeku esa firk vkSj iq=h dh mez dk vuqikr Kkr djsaA)                                         

(a) 17 : 5    (b) 25 : 17  (c) 17 : 6   (d) 17 : 3   (e) none of these

6. (i) The difference of present ages of A and B is 12 years. If 6 years back their ages were in the ratio 3 : 2, how old is A? (A vkSj B ds oÙkZeku mez dk varj 12 lky gSA ;fn 6 lky igys budh mez dk vuqikr 3 % 2 jgk gks( rks A dh orZeku mez D;k gS\)                                                                                                                       

(a) 24 yrs  (b) 42 yrs  (c) 32 yrs (d) Data inadequate  (e)none

(ii) Rahul is younger than Radha by 10 years. If 5 years back their ages were in the ratio 1:2, how old is Radha? (jkgqy jk/kk ls 10 lky NksVk gSA ;fn 5 lky igys budh mez vuqikr 1 % 2 Fkk( rks jk/kk dh mez Kkr djsaA)

a) 24 yrs    (b) 25 yrs   (c) 20 yr (d) Data inadequate   (e)none

(iii) The difference of present ages of A and B is 10 years. If 4 years back their ages were in the ratio 3 : 5, Find the sum of their present ages ? (A vkSj B dh mez dk varj 10 lky gSA ;fn 4 lky igys nksuksa dh mez dk vuqikr 3 % Fkk( rks oÙkZeku esa nksuksa dh mez dk ;ksxQy Kkr djsaA)             

(a) 24 yrs (b) 48 yrs  (c) 32 yrs  (d) Data inadequate     (e)none

PROBLEMS BASED ON AGES – 01

Question: One year ago the ratio between Samir’s and Ashok’s age was 4: 3. One year hence the ratio of their ages will be 5 : 4. What is the sum of their present ages in years?  (एक साल पहले समीर और अशोक की उम्रों का अनुपात 4 : 3 था. आज से एक साल बाद  समीर और अशोक की उम्रों का अनुपात 5 : 4 हो जाता है. उनकी वर्तमान उम्रों का योग बताइए.)   

(a) 15 yrs  (b) 13 yrs  (c) 20 yrs  (d) 16 yrs   (e) none of these

Ans. (d) 16 yrs

Solution:

Detailed explanation: First Method: When the differences between the terms of the ratios are the same, then this difference can be taken as equivalent to the real difference.

i. e., 5 – 4 = 4 – 3 = 1 ≡ 2 years (difference between the ages of one year ago and one year hence is 2)

Sum of the ages one year ago = 4 + 3 = 7 ≡ 14 years (as 1 ≡ 2 years)

So, the sum of the ages, at present = (14 + 2) = 16 years  

Or,

Sum of the ages one year hence = 5 + 4 = 9 ≡ 18 years (as 1 ≡ 2 years)

So, the sum of the ages, at present = (18 - 2) = 16 years

Second Method: Let the ages of Samir and Ashok, one year ago are 4x and 3x. So, their present ages, one year hence will be 4x +2 and 3x + 2. But this ratio is given as 5 : 4

 

 So, (16 – 15) x = 2 × (5 - 4); therefore, x = 2 years

Sum of the ages one year ago = 4x + 3x = 7x = 7 × 2 = 14 years

So, the sum of the ages, at present = (14 + 2) = 16 years