Concept of “Simple Interest”-09

Question: In certain years, a sum of money is doubled itself at 6.25 % simple interest per annum, then the required time will be [SSC (CGL), 2015 Tier-1]  [Ans. (d) 16 years]

(a) 12.5 years   (b) 8 years (c) 10  years (d) 16 years

Detailed Explanation: Concept: 1. “In simple interest, “Principal” remains constant throughout the period."

2. “Rate of simple interest is the interest on rupees 100 for one year”

First Method: Let Principal = 100, then the Amount = 200 and SI = 200-100=100

The Rate of interest is 6.25% pan, i. e., Rs 6.25 is SI on Rs. 100, so Rs.100 will be obtained in (100/6.25 )= 16 years

Second Method: Let Principal = P, Amount = A. Then, given that

Concept of “Simple Interest”-08

Question: A man invests an amount of Rs. 15860 in the names of his three sons A, B, and C in such a way that they get the same amount after 2, 3 and 4 years respectively. If the rate of simple interest is 5% pan, then what is the difference between the amounts invested in the names of A and C? [Ans. (c) Rs. 460]

(a) Rs.480 (b) Rs.960 (c) Rs.460 (d) Rs.260 (e) none of these

Solution:

Detailed Explanation: Let x, y and z are respectively the three parts of the total investments of Rs.15860, that the man invested in the names of his three sons A, B and C. The simple interest rate is 5% pan. Given that the amount of the investments in the names of A, B and C made for 2, 3 and 4 years respectively are equal.

So, x +y + z = 15860

And also, 110% of x = 115% of y = 120% of z

Or, 22×x= 23×y = 24×z

Dividing throughout by 22×23×24, we get

x/(23×24) = y/(22×24) = z/(22×23)

Or, x/(23×12) = y/(11×24) = z/(11×23)

Or, x: y: z = 276: 264: 253

Now, 793 ≡ Rs.15860 [total investments]

1 ≡ Rs.20

23 ≡? = Rs.460 [difference between A (276) and C (253)]

Ans.

Concept of “Simple Interest”-07 [IBPS-2014]

Question: The simple interest obtained when a certain sum of money is invested in scheme A for 3 years is Rs.38.8 less than the simple interest obtained when the same sum of money is invested in scheme B for 4 years. If the rates of interest offered by scheme A and scheme B are 14% pa and 12.5% pa respectively, how much money was invested in these schemes individually?

[Ans. (e) (Rs. 485)]

(a) Rs. 440 (b) Rs. 450 (c) Rs. 490 (d) Rs. 475 (e) Rs. 485 

Solution:

Detailed Explanation: A certain sum of money is invested in scheme at the rate of 14% pa for 3 years and the same capital is invested in scheme B at the rate of 12.5% for 4 years. That is, the interest obtained from scheme A is 42%, while interest obtained from scheme B is 50%. The difference is 8%, while the difference is given as Rs. 38.8.

So, 50% - 42% ≡ Rs. 38.88% [(12.5×4 - 14×3) % = (50-42) % = 8%]

Or, 8% ≡ Rs. 38.8

Or, 100% ≡? = Rs. 485 Ans.

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Simple Interest [साधारण ब्याज-06

Question: A certain sum is invested for certain time. It amounts to Rs. 80 at 5% per annum. But when invested at 2% per annum, it amounts to Rs. 40. Find the time?[Ans.(a)100 yrs]

(a) 100 years (b) 120 years (c) 90 years (d) 110 years (e) None of these

Solution: 

Detailed Explanation: Let a certain sum “P”, invested for a certain time “t” years, becomes Rs. 80 at 5% pan and Rs. 40 at 2% pan.

Therefore, (100+5t) % of P = 80 and (100+2t) % of P = 40

So, [(100+5t) % of P]/[ (100+2t) % of P] = 80/40 or (100+5t)/(100+2t) = 2/1 or,

t = 100 years                       

Simple Interest [साधारण ब्याज-05

Question: The simple interest on a certain sum of Rs. 160 is Rs. 40, and the number of years is equal to the rate percent per annum. Find the rate percent.  [Ans. (b) 5%]

(a) 5.5%    (b) 5%    (c) 8%   (d) 6%    (e) none of these

Solution:

Detailed Explanation: Rs. 40 is the simple interest of Rs. 160, so SI is ¼ th of the principal, which is 25%. Since the number of years is equal to the rate percent per annum, so (25)^1/2 = 5 is the required numerical value. Therefore, rate is 5% pan or time is 5 years. Ans.

Simple Interest [साधारण ब्याज-04

Question: A man had Rs. 2000, part of which he lent at 5% and the rest at 4%. The whole annual interest is Rs. 92. The money he lent at 5% was…..   [एक व्यक्ति के पास 2000 रु थे; जिसका एक भाग उसने 5% की दर से तथा शेष भाग उसने 4% की दर से लगाया. यदि उसे वार्षिक साधारण ब्याज 92 रु मिला हो, तो बताएं कि 5% की दर पर, उसने कितना धन लगाया था?]        [Ans. (c) (Rs. 1200)]

(a) Rs. 1000      (b) Rs. 1500       (c) Rs. 1200       (d) Rs. 2000       (e) none of these

Solution:

  

Detailed Explanation: We can solve this problem by method of “Alligation”. Method of Alligation can be used by two ways.

First Method: By method of Alligation, one part of the total sum of Rs.2000 is invested at the simple interest rate of 5% pan; while another part, at the simple interest rate of 4% pan. Here, the rate is taken as per hundred. In one year the SI is Rs. 92, which is 4.6% of Rs. 2000 and this, is the mean rate.

Ratio of investments at 5% and 4% is = (92-80) : (100-92) = 12 : 8 = 3 : 2

     Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

                                 By method of Alligation          

                                                      Rs. 2000     

                                      I (%/pan)             II (%/pan) 

                                           5                              4     

                                                Mean (%/pan)

                                                (92×100)÷2000

                                                       = 4.6 

                                      0.6 (4.6-4)     :        0.4 (5-4.6)

                                    Or,   3             :           2 

           

     Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

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Second Method: By method of Alligation, one part of the total sum of Rs.2000 is invested at the simple interest rate of 5% pan; while another part, at the simple interest rate of 4% pan. Here, the rate is taken as per hundred. In one year the SI is Rs. 92, which is 4.6% of Rs. 2000 and this, is the mean rate.

Ratio of investments at 5% and 4% is = (92-80) : (100-92) = 12 : 8 = 3 : 2

     Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

            Second Method

        By method of Alligation

                     Rs. 2000

        I (1/2000)             II (1/2000)                                 

            100                        80 

                Mean (1/2000)

                         92

          12 (92-80):        8 (100-92) 

             or, 3       :        2     

Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

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Third Method : Let the part of Rs. 2000 invested at the simple interest rate of 5% pan is Rs. “x”; then the other part of Rs.2000 is Rs. (2000-x), which is invested at the simple interest rate of 4% pan. Since the annual interest from both the parts together is Rs. 92, so

5% of x + 4% of (2000-x) = 92

1% of x = 12

100%of x = Rs. 1200 Ans.

Simple Interest [साधारण ब्याज-03

Question: At a certain rate of simple interest Rs. 800 amounted to Rs. 920 in 3 years. If the rate of interest be increased by 3%, what will be the amount after 3 years? [साधारण ब्याज की एक विशेष दर से 3 वर्षों में 800 रूपये बढ़कर 920 रूपये हो जाता है. यदि ब्याज की दर में 3% की वृद्धि होती है, तो बताएं कि 3 वर्षों के बाद मिश्रधन कितना हो जायेगा?] [Ans. (b) Rs. 992]

(a) Rs. 929  (b) Rs. 992  (c) Rs. 892  (d) Rs. 982 (e) None of these

Detailed Explanation: Since principal and time remain the same, and only rate is increased by 3%,  so at the rate of 3% pan and for the period of 3 years; the extra interest generated (3% × 3 = 9%) only is to be paid in addition to the amount (Rs. 920)  paid earlier. There is no need to calculate the rate of interest.

Principal is always taken as 100% and simple interest is calculated on the basis of principal (assuming it as 100% always) not on the basis of amount.

First Method:

                                          100% ≡? = Rs. 800

                                              9% ≡? = Rs. 72

                                       Required Amount = Rs. (920 + 72) = Rs. 992 Ans.

Second Method:

                                                   9% of Rs. 800 = Rs. 72

                                         Required Amount = Rs. (920 + 72) = Rs. 992 Ans.

Third Method: Rs. 800 becomes in Rs. 920 in 3 years, so the simple interest in 3 years is Rs. 120. The simple interest in one year is Rs. 40, which is 5% of Rs. 800 (As 100% ≡ Rs. 800, or it means 10% ≡ Rs. 80, or it means 5% ≡ Rs. 40). If the rate of interest is increased by 3%, then the new increased rate of interest is 8% pan. In three years, the S.I. (Simple Interest) will be 24%

                                          100% ≡ Rs. 800

                                            25% ≡ Rs. 200

                                              1% ≡ Rs. 8                               

                                         So, 24% ≡ Rs. 192                    

                                          Required Amount = Rs. (920 + 72) = Rs. 992 Ans.

Or, we can proceed as

                                          100% ≡ Rs. 800

                                            20% ≡ Rs. 160   (since, 10% ≡ Rs. 80)

                                              4% ≡ Rs. 32     (since, 1% ≡ Rs. 8)                               

                                      So, 24% ≡ Rs. 192                    

                                 Required Amount = Rs. (920 + 72) = Rs. 992 Ans.

9. SIMPLE INTEREST [साधारण ब्याज] - 1st part

1. (i) Find the SI on Rs 400 for 5 yrs at 6% pan. 

(a) Rs.120  (b) Rs.100  (c) Rs.150 (d) Rs.110 (e)none of these

(ii) A sum of Rs. 800 is lent for one year at the rate of 18% per annum. Find the interest. 

(a) Rs.140  (b) Rs.100  (c) Rs.142  (d)Rs.136 (e)none of these

(iii) A sum of Rs. 4000 is lent for 5 years at the rate of 15% per annum. Find the interest. 

(a) Rs2000 (b) Rs1000  (c)Rs.3000  (d)Rs3300  (e) none of these

(iv) The simple interest on Rs. 500 for 6 years at 5% per annum is 

(a) Rs.150  (b) Rs.120 (c) Rs.150  (d) Rs.200 (e)none of these

(v) The simple interest on Rs. 471 for 7 months at 2 paise/Re per month is 

(a) Rs.62.98  (b) Rs.72.64  (c) Rs.60.44   (d) Rs.65.94 (e) none

2. (i) What sum of money will produce Rs. 150 as interest in 2 years at 5 percent simple interest rate ? 

(a)Rs.1600  (b)Rs.1050 (c)Rs.1500 (d)data inadequate (e)none

(ii) A certain sum of money is borrowed by a person at 12% SI. If he has to pay Rs.5400 as interest after 3 yrs, then find the original sum? 

(a) Rs.2000  (b) Rs.10000 (c) Rs.20000 (d) Rs.15000  (e)none

(iii) What sum of money will produce Rs 150 as interest in 6 months at 4 percent simple interest rate? 

(a) Rs 5600  (b) Rs 7500  (c) Rs 10000  (d) Rs 15000  (e) none

(iv) The sum of money that will pay Re 1 as interest per day at 5% pan simple interest is 

(a)Rs.7300 (b)Rs.3650 (c)Rs.3700  (d)Rs.200 (e)none of these

(v) The SI at x% pan for ‘x’ years will be Rs ‘x’ on a sum of 

(a) Rs. (100/X)  (b) Rs. x   (c) Rs 100x   (d) Rs 100/(square of x)    (e) none of these

3. (i) A certain sum of money is borrowed by a person at 4% p.a. simple interest for 5 years. If he has to pay Rs. 160 as interest, find the total amount he has to pay.   

(a) Rs.690 (b) Rs.950 (c)Rs.86 (d) Rs. 960 (e) none of these 

(ii) A certain sum of money is borrowed by a person at 5% simple interest for 5 years. If he has to pay Rs. 100 as interest, find the total amount he has to pay. 

(a) Rs.500 (b) Rs.450 (c) Rs. 600 (d) Rs. 520 (e) none of these

(iii) A sum of money which increase 1/10 of itself every year amounts to Rs. 450 in 5 years is… 

(a) Rs.300  (b) Rs.200 (c) Rs.250 (d) Rs.350 (e) none of these

4. (i) In what time will Rs. 500 amount to Rs. 625 at 5% per annum? 

(a) 6 years(b) 10 years (c) 5 years (d) 12 years(e) none of these 

(ii) In how many years will Rs. 300 amount to Rs. 405 at 5%? 

(a) 6 years(b) 10 years(c) 7 years(d) 5 years (e) none of these

(iii) In what time will Rs. 8500 amount to Rs. 15767.50 at 4 ½ % per annum ?        [Ans. (c) 19 years]

(a) 16 years(b) 20 years (c) 19 years(d) 15 years (e) none of

(iv) In what time will the SI be 2/5^th of the principle at the rate of 8% pan. [Ans.(c)5 yrs]

(a) 8 years(b)  7 years (c)  5 years(d) 6 years(e) none of these 

5. (i) At what rate percent per annum will the simple interest be 1/5th of the principal in 4 years?  [Ans. (b) 5%]

(a) 4%  (b) 5%    (c) 6%      (d) 8%          (e) none of these

6. (i) A man buys land and gives for it 20 times the annual rent. The rate of interest does he get for his money, is…. 

(a) 4%      (b) 5%      (c) 6%        (d) 8%       (e) none of these

7. (i) If a bank pays 15% dividend, what rate of interest would a man get by purchasing Rs.10 shares for Rs.12 ?

(a) 10%  (b) 12.5% (c) 15% (d) 20%   (e) none of these

8. (i) At what rate percent will Rs. 425 amount to Rs. 476 in 3 years?   [Ans. (c) 4%]

(a) 5%     (b) 6%      (c) 4%      (d) 3%        (e) none of these

(ii) A borrowed Rs. 5000 from B at simple interest. After 4 years, B received Rs. 1000 more than the amount given to B on loan. The rate of interest was:         [BSRB Exam, 1991]            

(a) 7%       (b) 6%        (c) 4%         (d) 5%    (e) none of these

(iii) If Re. 1 produces Rs 9 as interest in 60 years at SI, the rate percent is:    [Ans. (c) 15]

(a) 12           (b) 10      (c) 15        (d) 16        (e) none of these

(iv) A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 3 months. The rate of interest per annum is :  [Ans.(d) 7 %]

 (a) (5 and 1/2)%    (b) 8%      (c) 6%         (d) 7%     (e) none of these

9.(i)At what rate percent simple interest will a sum of money double itself in 20 years?  [Ans.(c) 5%]

(a) 3%      (b) 4%          (c) 5%        (d) 6%     (e) none of these 

(ii) At what rate percent simple interest will a sum of money double itself in 8 years?   [Ans. (a) 12.5%]

(a) 12.5%    (b) 10.5%     (c) 5%     (d) 6%     (e) none of these

(iii) At what rate percent simple interest will a sum of money be 7/6 times itself in 3 years?             

(a) (5 and 5/9)%  (b)  (6 and 5/9)% (c) 18%   (d) 25%   (e) none of these

(iv) A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?   [Ans.(b) 10%]

(a) 15%     (b) 10%   (c) 12%      (d) 11%      (e) none of these

(v) A sum of money trebles itself in 25 years at simple interest. What is the rate of interest? [Ans.(b) 8%]

(a) 10%     (b) 8%     (c) 12%       (d) 6%       (e) none of these

(vi) A sum of money becomes 6 times in 20 years at simple interest. What is the rate of interest?  [Ans. (d) 25%]

(a) 20%     (b) 30%   (c) 27%       (d) 25%     (e) none of these

(vii) At what rate percent (simple interest) will a sum of money double itself in 16 years ? [Ans.(d) 6 ¼ %] 

(a) 50%     (b) 5%     (c) 10%       (d) 6 ¼ %  (e) none of these

10. (i) In what time does a sum of money become 4 times at the simple interest rate  of 5% per annum?  [Ans.(c) 60 years]

(a) 65 years  (b) 50 years   (c) 60 years   (d) 70 years  (e) none

(ii) In what time does a sum of money become 3 times at the simple interest rate of 8% per annum?  [Ans. (a) 25 years]

(a) 25 years  (b) 20 years  (c) 30 years  (d) 27 years    (e) none

11. (i) A sum of money becomes four times at the simple interest rate of 5% per annum. At what rate percent will it become seven fold?   [Ans. (b) 10%]

(a) 15%     (b) 10%     (c) 12%      (d) 20%     (e) none of these

 

(ii) A sum of money becomes 6 times at the simple interest rate of 5% per annum. At what rate percent will it become twelve fold?    [Ans. (c) 11%]

(a) 15%    (b) 10%      (c) 11%     (d) 12%      (e) none of these

12. (i) A sum of money becomes 5 times at simple interest in 8 years. In how many years will it be 7 fold? [Ans. (b)12 yrs]

(a) 10 years (b) 12 years    (c) 8 years   (d) 15 years    (e) none

(ii) A sum of money becomes 2 times at simple interest in 2 years. In how many years will it be five fold?  [Ans.(c) 8 yrs]

(a) 10 years   (b) 12 years   (c) 8 years    (d) 15 years  (e) none

(iii) A sum of money doubles itself in 4 years at a simple interest. In how many years will it amount to 8 times itself?                                                                     

 (a) 20 years   (b) 12 years   (c) 30 years   (d) 15 years (e)none

(iv) If a sum of money at simple interest doubles in 5 years, it will becomes 4 times in how many years? 

(a) 15          (b) 20          (c) 18          (d) 16           (e) none of these

13. (i) If the simple interest on Rs. 2000 increases by Rs 40, when the time increases by 4 years. Find the rate percent per annum.   [Ans. (d) 0.5%]

(a) 5%      (b) 0.25%   (c) 1%       (d) 0.5%     (e) none of these

(ii) If the simple interest on Rs. 170 increases by Rs 17, when the time increases by 5 years. Find the rate percent per annum.                                                                                                             

(a) 1.5%     (b) 2%     (c) 1%        (d) 2.5%    (e) none of these

Simple Interest - 02

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 interests is Rs. 42, find each sum.          

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

Solution:  [Detailed Explanation: 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%

In another way, it can also be understand as : 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%. Therefore,

Simple Interest - 01

Question:  A certain sum of money amounts to Rs. 560 in 3 years at 4% per annum simple interest?   Find the sum.                                                       

(a) Rs. 500        (b) Rs. 475         (c) Rs. 450         (d) Rs. 560           (e) none of these

Solution: Detailed Explanation: Principal is always taken as 100%

Since rate of interest is 4% per annum, so in 3 years, simple interest will be (4 × 3) % = 12%

Amount is (100 + 12) = 112% Therefore,