SBI PO – 2015 – 34

Question: A reduction of 20% in the price of salt enables a person to buy 8 kg more for Rs. 80. Find the reduced and the original price per kg of salt respectively. [नमक के मूल्य में 20% की कमी होने पर एक व्यक्ति 80 रूपये में 8 किग्रा नमक ज्यादा खरीद पाता है. नमक का घटा हुआ एवं प्रारंभिक मूल्य प्रति किग्रा क्रमशः बताएं.]      [Ans. (c) Rs. 2, Rs. 2.50]                                                                 

(a) Rs 2.50, Rs.2 (b) Rs 2.50, Rs 3 (c) Rs 2, Rs 2.50 (d) Rs 1.5, Rs 2 (e) None of these

Detailed Explanation:

First Method: Price of salt reduces by 20%, so 20% of Rs 80 = Rs 16

Extra salt available is 8 kg, when price reduces by 20%

So, 8 kg of salt costs Rs 16, then 1 kg of salt cost Rs 16/8 = 2 Rs/kg; which is reduced price Ans.

Now the Original Price can be determined by two methods

First Method

Second Method

Since reduction is 20%,

80 % ≡ 2 Rs/kg (Reduced Price)

100% ≡? = 2.50 Rs/kg (Original Price) Ans.

Second Method: Let the rate of salt is x Rs/kg.

When the price of salt reduces by 20%, the reduced rate becomes 80% of x = 4x/5 Rs/kg.

Initial quantity was 80/x kg; while quantity at the reduced rate is 80/(4x/5) kg. The difference is of 8 kg. So,

      

SBI PO – 2015 – 33

Question: An article is sold at a discount of 20% on the marked price. In order to gain 60% on marked price, at how many more percent of the discounted price, it should be sold? [एक वस्तु अंकित मूल्य पर 20% बट्टे पर उपलब्ध है. अंकित मूल्य पर 60% लाभ कमाने के लिए, बट्टे पर उपलब्ध वस्तु के मूल्य में कितने प्रतिशत की वृद्धि करनी चाहिए?] [Ans. (e) None of these (100%)]

(a) 75%     (b) 25%    (c) 65%   (d) 200%   (e) None of these

Solution:

Detailed Explanation:

First Method: Let marked price (MP) be 100. Since 20% discount is given on marked price, so discounted selling price is 80% of 100, which is 80.

If 60% profit is to be earned on marked price, then it must be 100 + 60% of 100 = 160

If 80 is to be 160, so it should be 200%. That is, there should be an increase of 100%. Ans.

Second Method: Let marked price (MP) be 100. Since 20% discount is given on marked price, so discounted selling price is 80% of 100, which is 80.

If 60% profit is to be earned on marked price, then it must be 100 + 60% of 100 = 160

If 80 is to be 160, so it should be 200%. That is, there should be an increase of 100%. Ans.

Third Method: When any quantity is changed by x% and y% successively, then the quantity is changed by

SBI PO – 2015 – 32

Question: The average of 7 consecutive odd numbers is 47. What is the greatest number among these seven numbers? [7 क्रमागत विषम संख्याओं का औसत 47 है. इन सात संख्याओं में सबसे बड़ी संख्या क्या है?] [Ans. (b) 53]

(a) 35      (b) 53     (c) 52     (d) 63     (e) None of these

Detailed explanation:

First Method: For any arithmetic series, middle term is the average of the series (if number of terms is odd).

For seven consecutive odd numbers, middle term, i. e., 4^th term is the average. Given that 47 is the average of the seven consecutive odd numbers, so 4^th term is 47.

Greatest number is 7^th term, which is 6 (2 × 3 = 6) more than 4^th term.

Therefore, greatest number is, 47 + 6 = 53. Ans.

Second Method: Let the seven consecutive odd numbers are (x - 6), (x - 4), (x - 2), x, (x + 2), (x + 4) and (x + 6)

Average of seven numbers is given 47; while no. of numbers is 7

Since, sum = average × number of item

So, (x - 6) + (x - 4) + (x - 2) + x + (x + 2) + (x + 4) + (x + 6) = 47 × 7

Or, 7x = 47 × 7, which implies that x = 47

Greatest of seven number = x + 6 = 47 + 6 = 53 Ans.

SBI PO – 2015 – 31

Question: Ramesh can row a certain distance downstream in 6 hrs and return the same distance in 9 hrs. If the stream flows at the rate of 3 km/h, find the speed of Ramesh in still water. [रमेश धारा की दिशा में एक निश्चित दूरी को 6 घंटे में तय कर लेता है, जबकि वापसी में उसी दूरी को तय करने में उसे 9 घंटे लगते हैं. यदि धारा 3 किमी/घंटे की चाल से बह रही हो, तो शांत जल में रमेश की चाल बताएं.]      [Ans. (b) 15 km/hr]

(a) 6 km/h  (b) 15 km/h  (c) 8 km/h  (d) 9 km/h   (e) None of these

Detailed explanation:

First Method: Let “X” and “Y” are the speeds of Ramesh along downstream and upstream respectively. Since distance is the same; so speeds will be in the inverse ratio of time taken.

Also, speed of a man downstream, X = u + v

And, speed of a man upstream, Y = u - v

So, X : Y = 9 : 6

It means (u + 3) : (u - 3) = 3 : 2 That is, (u + 3) / (u - 3) = 3 / 2. Or, u = 3 × 5 = 15 km/h Ans.

Second Method: Since distance is the same; so speeds will be in the inverse ratio of time taken.

Also, speed of a man downstream, X = u + v

And, speed of a man upstream, Y = u - v

So, X : Y = 9 : 6 = 3 : 2

u : v = X + Y : X – Y = 3 + 2 : 3 – 2 = 5 : 1

But, “1” is the speed of current and it is given as 3 km/h.

So, “3” is the speed of Ramesh, that must be 3 × 5 = 15 km/h Ans.

Third Method : We know that

Distance = speed × time

Downstream speed is X and time taken is 6 hours; while upstream speed is Y and time taken is 9 hours.

Also, X = u + v and Y = u - v

Therefore, (u + 3) × 6 = (u - 3) × 9

Or, (u + 3) × 2 = (u - 3) × 3

Or, u = 3 × 5 = 15 km/h Ans.

SBI PO – 2015 – 30

Question: Weight of two persons A and B are in the ratio of 3 : 5. A’s weight increases by 20% and the total weight of A and B together becomes 80 kg, with an increase of 25%. By what percent did the weight of B increase? [दो व्यक्तियों A तथा B के वजन का अनुपात 3 : 5 है. A का वजन 20% से बढ़ जाता है. यदि दोनों के कुल वजन में 25% की वृद्धि होती है, और यह बढ़कर 80 किग्रा हो जाता है, तो, बताएं कि B के वजन में कितने प्रतिशत की वृद्धि होती है?] [Ans. (a)  28%]

(a)  28% (b)  30%  (c)  45%   (d) 32%     (e) none of these

Detailed Explanation:

First Method: The question can be easily be solved by “Method of Alligation”. Since A’s weight increases by 20%, while total weight increases by 25%. The ratio between the weights is 3 : 5.

The difference between 20 and 25 is 5 and the term of the ratio for B is also 5. So, 5≡5

The term of the ratio for A is 3. So, 3 ≡ 3

Since 20 is less than 25, so “?” (percentage increase in B) must be greater than 25 by 3.

Therefore, ? – 25 = 3. It means, ? = 28. So, 28% Ans.

Second Method: “Without changing the ratio, the values may be changed”.  Since the ratio between the weights of A and B is 3 : 5, so let the weight of A is 300 kg and weight of B is 500 kg; so that the total weight of A and B becomes 800 kg.

Increase in A’s weight = 20% of 300 kg = 60 kg

Increase in total weight = 25% of 800 kg = 200 kg

Increase in B’s weight = 200 kg – 60 kg = 140 kg

140 is the increase out of 500, that is 28% Ans. 

SBI PO – 2015 – 29

Question: A man bought 13 shirts of Rs. 50 each, 15 pants of Rs. 60 each and 12 pairs of shoes at Rs. 65 a pair. Find the average value of each article [एक व्यक्ति ने 50 रु की दर से 13 कमीज ख़रीदे; 60 रु की दर से 15 पैंट्स ख़रीदे और 65 रु की दर से 12 जोड़ी जूते ख़रीदे. उन सभी वस्तुओं का औसत निकालें] [Ans. (a) 58.25]                            

(a) 58.25  (b) 56.75 (c) 50.25 (d) 60.25 (e) none of these

Detailed explanation:

First Method: Let the average of all articles be 50. Since the average of 15 pants is 60, so in the group of 15 pants, there are 15 × 10 = 150 Rs are extra. And, in the group of 12 pairs of shoes, there are 12 × 15 = Rs 180 extra. So, there are a total of Rs (150 + 180) = Rs 330 extra, that is to be distributed among all the 40 articles equally. In this way, each of the article will get (Rs 330)/40, that is, Rs 8.25 additionally.

Therefore, the average = Rs (50 + 8.25) =Rs 58.25 Ans.    

First method is the best method.

Second Method: This is usual method.

Price of 13 shirts at the rate of 50 Rs/shirt = Rs 50 × 13 = Rs 650  

Price of 15 pants at the rate of 60 Rs/pant = Rs 60 × 15 = Rs 900  

Price of 12 pairs of shoes at the rate of 65 Rs/pair = Rs 65 × 12 = Rs 780  

Average of all articles = (Rs 650 +Rs 900 + Rs 780)/ (13 + 15 + 12)

Rs 2330/ 40. Therefore average = 58.25 Ans.

SBI PO – 2015 – 28

Question: A train passes by a stationary man standing on the platform in 7 seconds and passes by the platform completely in 28 seconds. If the length of the platform is 330 meters, what is the length of the train? [एक पैसेंजर प्लेटफार्म पर खड़े एक व्यक्ति को 7 सेकेण्ड में तथा पूरे प्लेटफार्म को वह 28 सेकंड में पार कर लेती है. यदि प्लेटफार्म की लम्बाई 330 मीटर हो; तो ट्रेन की लम्बाई बताएं.]   [Ans. (d)110 m.]

(a) 120 m.     (b) 100 m.    (c) 80 m.     (d) 110 m.   (e) None of these

Detailed  Solution: When a train crosses a man, it means it describes a distance equal to its length in that given time. But, when a train crosses a platform, it means it describes a distance equal to the sum of the length of the train and platform.

First Method: Since here, a train passes by a stationary man standing on the platform in 7 seconds and passes by 

the platform completely in 28 seconds; so the train describes a distance of 330 meter (length of train) in 21 sec (28 - 7). That is, 110 meter in 7 sec, which is the length of the train.

Second Method: Let the length of the train be ‘L’ m.

Since the train crosses a man in 7 sec, so the speed of the train = L/7 m/s

Again, since the train crosses a platform in 28 sec completely, so the speed of the train = (L + 330)/28

So, L/7 = (L + 330)/28, so solving them, we get L = 110 meter Ans.

Third Method: Let the speed of the train be “u” m/s.

Since the train crosses a man in 7 sec, so the length of the train = 7u meter

Again, since the train crosses a platform in 28 sec, so the sum of the length of the train and platform = 28u meter

Therefore, length of the platform = 28u – 7u = 330

Or, 21u = 330, that means, length of the train = 7u = 110 meter Ans.

SBI PO – 2015 – 27

SIMPLIFICATION  

Q. 12 × 3.5 – 8.5 × 3.2 =?

(1) 14.8      (2) 18.4       (3) 69.2       (4) 16.8       (5) None of these

 

Detailed explanation: 

12 × 3.5 – 8.5 × 3.2 =?  

Or, 6 × 7 – 17 × 1.6 =? 

Or, ? = 42 – 27.2 = 14.8 Ans.

Explanation: 12 × 3.5 = 6 × (2 × 3.5) = 6 × 7                                                              

Similarly, 8.5 × 3.2 = (8.5 × 2) × 1.6 = 17 × 1.6                                       

Also, 17 ×1.6 = 17 × (1 + 0.6) = 17 + 10.2 = 27.2                                  

[Note: When 5 occurs at the unit place, it is to be doubled, so as to get '0' at the unit place and the number becomes easy to multiply]

     

SBI PO – 2015 – 26

SIMPLIFICATION

SBI PO – 2015 – 25

SIMPLIFICATION

SBI PO – 2015 – 24

SIMPLIFICATION

SBI PO – 2015 – 23

Question: A person invested a certain amount at simple interest at the rate of 6% per annum earning Rs. 900 as an interest at the end of 3 years. Had the interest been compounded every year, how much more interest would he have earned on the same amount with the same interest rate after three years? 

[6% प्रति वर्ष साधारण ब्याज की दर से 3 वर्षों में किसी मूलधन का साधारण ब्याज 900 रुपये मिलता है. यदि उस व्यक्ति ने वाही धन समान समय के लिए और समान दर पर चक्रवृधि ब्याज पर लगाया होता, तो उसे कितना ब्याज ज्यादा मिलता; जबकि ब्याज वार्षिक संयोजित होता हो?]                           [Ans. (d)  Rs. 55.08]

(a) Rs 38.13  (b) Rs 25.33 (c) Rs 35.03  (d) Rs 55.08 (e) none of these

                                                                                               

Detailed explanation: Since Rs 900 is the simple interest for 3 years, so Rs 300 is the simple interest for each of the 3 years.       

Difference for the first year = Rs 0

Difference for the second year = 6% of Rs 300 = Rs 18

Difference for the third year = 6% of Rs 300 + 6% of Rs 300 + 6% of Rs 18 = Rs 18 + Rs 18 + Rs 1.08 = Rs 37.08

Therefore,  total differences in three years = Rs 18 + Rs 37.08 = Rs 55.08 Ans. 

SBI PO – 2015 – 22

Question: A shopkeeper sold an item for Rs 6080 after giving 20% discount on the labeled price and made 18% profit on the cost price. What would have been the percentage profit if he had not given the discount? [एक दुकानदार एक सामान को अंकित मूल्य पर 20% का बट्टा देते हुए 6080 रूपये में बेचता है; जिससे उसे 18% का लाभ होता है. दुकानदार का प्रतिशत लाभ बताएं, यदि बट्टा नहीं दिया जाता?] 

Ans. (2) 47.5%

1) 45.5%    (2) 47.5%     (3) 55%     (4) 42%        (5) 54%

Solution:

Detailed Explanation:

First Method: Let cost price (CP) be 100. The article is sold at a profit of 18%, so the selling price is 118% of 100 = 118.  

Next, the discount given is 20% on the label price. If we assume label price as 100%; then selling price is 80%, that is 118. So, 100% is 147.50. In other words, it can be said as – “80% is equivalent to 118, so 100% is equivalent to what?” If discount is not given on label price, then label price will be the selling price, that is, 147.5%. Therefore, profit percent is 47.5% Ans.

Second Method: Here, CP is increased by x% to get label price, and label price is reduced by 20% (discount); so that selling price is obtained (18% above the cost price). When discount is not given, then label price becomes selling price, and x% becomes profit percent.

SBI PO – 2015 – 21

Question:  Two equal amount of money are deposited in two banks each at 5% per annum for 3 and 4 years respectively. If the difference between their simple interests is Rs. 42, find each sum. [5% प्रति वर्ष साधारण व्याज की दर से 3 तथा 4 वर्षों के लिए किसी समान धन के साधारण ब्याज का अंतर 42 रूपये है; तो वह धन क्या है?]  Ans. (d) Rs. 840         

(a) Rs. 210        (b) Rs. 280      (c) Rs. 750      (d) Rs. 840     (e) none of these

 

Detailed Explanation:

First method: Principal is always taken as 100%

Since rate of interest is 5% per annum, so interest for one year (4 - 3) will be 5% × 1 = 5%

5% is equivalent to Rs 42, so 100% will be 20 times of Rs 42, that is Rs 840 Ans.

Second Method: At the rate of 5% per annum, the SI for 3 years is 15% and SI for 4 years is 20%, so the difference is (20 -15)% = 5%. 5% of Principal = Rs 42. So, Principal is (42×100)/5   = Rs 840 Ans.

Third Method: Using (PRT/100), we solve as shown above.

SBI PO – 2015 – 20

Question: The average age of 34 boys in a class is 28.5 years. If the teacher’s age is included, the average age of the boys and the teacher becomes 29 years. What is the teachers’ age? [किसी कक्षा के 34 छात्रों की औसत आयु 28.5 वर्ष है. यदि शिक्षक की आयु भी शामिल कर ली जाये, तो शिक्षक सहित छात्रों की औसत आयु 29 वर्ष हो जाती है. शिक्षक की आयु क्या है? ]  Ans. (c) 46 year

(a) 45 year   (b) 46.5 year   (c) 46 year   (d) 45.5 years   (e) none of these 

Detailed solution:

First Method: Since the average age of students including teacher is 29 yrs, so the teacher should have 29 yrs at least. Also, to increase the age of the students from 28.5 to 29 yrs, that is, to increase the age of each of the 34 students by 0.5 yrs; he must have 17 yrs. So, the age of the teacher = 29 yrs + 17 yrs = 46 yrs Ans.   

Second Method: Age of the teacher = average age of students including teacher + difference between the averages × no. of students = 29 yrs + (29 – 28.5) × 34 yrs = 29 yrs + 0.5 × 34 = 29 yrs + 17 yrs = 46 yrs Ans.                          

            

Third Method: Age of the teacher = average age of students + difference between the averages × total no. of students including teacher = 28.5 yrs + (29 – 28.5) × 35 yrs = 28.5 yrs + 0.5 × 35 = 28.5 yrs + 17.5 yrs = 46 yrs Ans.                          

Fourth Method: Age of teacher = total age of students including teacher – total age of students = [29 × 35 – 28.5 × 34] yrs = [1015 – 969] yrs = 46 yrs Ans.  (Since sum = average × no.) (usual method)

SBI PO – 2015 – 19

Question: On what sum will the difference between the simple and compound interest for 2 years at 4% per annum amounts to Re.1, interest is compounded yearly. [किस मूलधन पर 4% वार्षिक की दर से 2 वर्षों में साधारण एवं चक्रवृधि ब्याज का अंतर 1 रूपये होगा; जबकि ब्याज वार्षिक संयोजित होता है?]    [Ans. (c) Rs 625].            

(a) Rs. 650    (b) Rs. 630   (c) Rs. 625  (d) Rs. 64   (e) none of these

Detailed explanation:

First Method :                                  

For the first year, there is no difference between SI and CI. So, the difference between SI and CI during the second year is the difference between SI and CI in two years.

Therefore, difference = Re 1 = 4%, where as the SI of the first year is 100%. So,   

                                               4% ≡ Re 1                                                                   

                                           100% ≡ ? = Rs 25 (SI)                                                                                                                            

Simple Interest thus obtained is 4% of the principal. So,

                                       (SI) 4% ≡ Re 25 (SI)                                                                   

                 (PRINCIPAL) 100% ≡ ? = Rs 625 Ans.                                                                                                                          

Second Method:  

Where P = principal, r = rate of interest

Third Method : If principal is Rs 100, then 4% of Rs 100 = Rs 4 is the simple interest for the first year. Difference for the second year is 4% of Rs 4 = 0.16. Therefore, 0.16% is the difference between CI and SI, where as 100% is the principal.

(diff.) = 0.16% ≡ Re 1

(principal) = 100% ≡ ? = Rs 625 Ans.

SBI PO – 2015 – 18

Question: Two train start at the same time from Hyderabad and Delhi and proceed towards each other at the rate of 80 km and 95 km per hour respectively. When they meet it was found that one train has travelled 180 km more than the other. Find the distance between Delhi and Hyderabad. [हैदराबाद एवं दिल्ली से दो ट्रेनें क्रमशः 80 किमी/घंटे तथा 95 किमी/घंटे की दर से एक दूसरे की ओर आ रही हैं. जब वे मिलती हैं, तो एक ट्रेन दूसरी ट्रेन से 180 किमी ज्यादा चल चुकी होती है. बताइए कि दिल्ली से हैदराबाद की दुरी क्या है?] Ans. (d) 2100 km 

(a) 2110 km  (b) 2000 km. (c)2200 km (d) 2100 km  (e) None of these

Detailed explanation:

First Method : Since both the train take the same time to meet. So, (x + 180)/95 is equal to x/80

Solving it, we get x = 960 km. Distance described by the trains from Delhi and from Hyderabad are respectively 960 km  and (960 + 180) km. that is, 960 km and 1040 km. Therefore, total distance = 2100 km Ans. [x is the distance described by the train coming from Hyderabad, when they meet.]  

  

Second Method : Since in the same time, one train describes 180 km more than the other, 

so 95t – 80t = 180 so, t = 12 h  Total distance = 175 × 12 = 2100 km Ans. [t is the time taken by each of the train.] 

Third Method : Since both the train take the same time to meet, so the ratio of the distance described by the train will same as the ratio of the speed of the trains. That is, in the ratio of 95 : 80, that is, in the ratio of 19 : 16.

Here, difference is 3, while the sum is 35.                                          

(diff.) 3 ≡ 180 km,    1 ≡ 60 km,  Total distance = 35 × 60 km = 2100 km Ans.

Fourth Method  Time = Since the speed of the trains are 80 and 95 km/h and one train describes 180 km more than the other in the same interval of time, so this 180 km is described by the trains at the rate of 15 km/h (95-80) in 12 hours (180 km/15 km/h).

The trains describe the distance between Delhi and Hyderabad at the rate of 175 km/h in 12 hours.

So, total distance = 175 km/h × 12h  = 2100 km Ans.  The best method [relative speed method]

SBI PO – 2015 – 17 [IBPS CWE (RRB Officers), 2014]

Question: The ratio of the base to the height of a right angled triangle is 4:5. If the area of the right angled triangle is 80 square cm, then what is the height of the triangle? [किसी समकोण त्रिभुज के आधार तथा ऊंचाई का अनुपात 4:5 है. यदि समकोण त्रिभुज का क्षेत्रफल 80 वर्ग से मी हो, तो बताएँ कि समकोण त्रिभुज की ऊंचाई क्या है?] Ans. (e) 

SBI PO – 2015 – 16 [IBPS CWE (RRB Officers), 2014]

Question: The numerical value of the area of a rectangular field is 90 times the numerical value of its breadth. If the perimeter of the field is 240 meter, what is the breadth of the field? [किसी आयताकार मैदान के क्षेत्रफल का संख्यात्मक मान, उसकी चौड़ाई के संख्यात्मक मान का 90 गुणा है. यदि मैदान की परिमिति 240 मीटर हो, तो मैदान की चौड़ाई कितनी है?] Ans. (c) 30 meter

(a) 60 meter (b) data inadequate (c) 30 meter (d) 20 meter (e) 15 meter

Detailed explanation: Given that the area of the numerical value of the area of a rectangular field is 90 times the numerical value of its breadth.

So, area = l × b = 90 × b. That is, l = 90

Given that perimeter = 2 (l + b) = 240. That is, l + b = 120

So, b = 120 – 90 = 30. Therefore, 30 meter is the answer.