SIMPLE INTEREST QUIZ 001

1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

(a) Rs. 650

(b) Rs. 690

(c) Rs. 698

(d) Rs. 700

(e) None of these

 

Answer Option :3

Solution »

S.I. for 1 year = Rs. (854 – 815) = Rs. 39.

S.I. for 3 years = Rs.  (39 x 3) = Rs. 117.

Principal = Rs. (815 – 117) = Rs. 698

 

2. What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and that for 9 years?

(a) 3:2

(b) 2:3

(c) 1:3

(d) Data inadequate

(e) None of these

 

Answer Option :2

Solution »

Let the principal be P and rate of interest be R%.

Required ratio =

(( P x R x 6 )/100)

= (6PR/9PR) = 6/9= 2 : 3.

 

3. What annual instalment will discharge a debt of Rs. 1,092 due in 3 years at 12% simple interest?

(a) Rs. 325

(b) Rs. 545

(c) Rs. 560

(d) Rs. 540

(e) None of these

 

Answer Option :1

Solution »

Let each instalment be Rs. x.

1st year = [x + (x * 12 * 2)/100]

2nd year = [ x + (x *12 * 1)/100]

3rd year = x

Then, [x + (x * 12 * 2)/100] + [ x + (x *12 * 1)/100] + x =1092

3x + ( 24x/100 ) + ( 12x/100 ) = 1092

336x =109200

x = 325

Each instalment = Rs. 325

 

4. Reena took a loan of Rs. 1,200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

(a) 3.6

(b) 6

(c) 18

(d) cannot be determined

(e) None of these

 

Answer Option :2

Solution »

Let rate = R% and time = R years.

Then, (1200 * R * R)\100 = 432

= R² = 36

= R = 6

 

5. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3,508, what was the amount invested in Scheme B?

(a) Rs. 6,400

(b) Rs. 6,500

(c) Rs. 7,200

(d) Rs. 7,500

(e) None of these

 

Answer Option :1

Solution »

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13,900 – x).

Then,

=> 28x – 22x = 350800 – (13900 x 22)

=> 6x = 45000

=> x = 7500.

So, sum invested in Scheme B = Rs. (13,900 – 7,500) = Rs. 6,400.

 

6. A father left a will of Rs. 35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs. 35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?

(a) Rs. 17.5 lakhs

(b) Rs. 21 lakhs

(c) Rs. 20 lakhs

(d) Rs. 15 lakhs

(e) Rs. 25 lakhs

 

Answer Option :2

Solution »

Let Rs. x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (3,500,000 – x).

7. How long will it take for a sum of money to grow from Rs. 1,250 to 10, 000, if it is invested at 12.5% p.a. simple interest?

(a) 56

(b) 45

(c) 68

(d) 78

(e) 43

 

Answer Option :1

Solution »

Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the number of years for which it is invested, r is the rate of interest per annum

In this case, Rs. 1,250 has become Rs. 10,000.

Therefore, the interest earned = 10,000 – 1,250 = 8,750.

8750 = [(1250*n*12.5)/100]

=> n = 700 / 12.5 = 56 years.

 

8. If the simple interest on a certain sum of money is 4/25 of the sum and the rate per cent equals the number years, then the rate of interest per annum is:

(a) 4%
(b) 5%
(c) 8%
(d) 10%
(e) None of these

 

Answer Option :1

Solution »
Let the principal be Rs x.
Then the SI =4/25x
Rate of interest = Time
r= (100*4/25x)/ x*r
r² =400/25

r=20/5=4%

 

9. A financier lend money at simple interest, but he includes the interest every six months for calculating the principal. If he is changing an interest of 10%, the effective rate of interest becomes?
   (a) 10%
   (b) 11.5%
   (c) 10.25%
   (d) 12%
   (e) None of these

 

Answer Option :3

Solution »
Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 10 * 1/2)/100] = Rs. 5
Next 6 months 10% of 5 is Rs. 2 is added.
S.I. for last 6 months = Rs. [(102 * 10 *1/2)/100] = Rs. 5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25
R = (110.25 – 100) = 10.25%

 

10. Ragav purchases a coat for Rs. 2,400 cash or for Rs. 1,000 cash down payments and two monthly instalments of Rs. 800 each. Find the rate of interest.
    (a) 80%
    (b) 100%
    (c) 110%
    (d) 120%
    (e) None

 

Answer Option :4

Solution »
Amount as a principal for 2 month = 2400 – 1000 = 1400
At the rate of r% per annum after 2 months,

D 1400 will amount to Rs 1400 + (1400*r*2/100*12)
Total amount for 2 instalments at the end of second month
D 800+(800+(800*r*1/100*12))
Then 1400 + 2800*r/1200=1600 + 800*r/1200
R=120%

 

11. Two persons P and Q borrowed Rs. 40,000/- and Rs. 60,000/- respectively from R at different rates of simple interest. The interest payable by P at the end of the first four years and that payable by Q at the end of the first three years is the same. If the total interest payable by P and Q for one year is Rs. 8,400/-, then at what rate did Q borrow the money from R?
    (a) 8
    (b) 10
    (c) 12
    (d) 9
    (e) None

 

Answer Option :1

Solution »
40000*4*R₁/100=60000*3*R₂/100
R₁=9/8R₂
1yr interest
40000*1*r₁/100+60000*1*R₂/100=8400
4R₂+6R₂=84
Then, substitute 4(9/8R₂)+6R₂=84==>
R₂=8

 

12. The rate of interest on a sum of money is 4% per annum for the first 2 years, 6% per annum for the period next 4 years, 8% per annum for the period beyond 6 years. If the simple interest accrued by the sum for a total period of 9 years is Rs. 1680, what is the sum?
    (a) Rs. 3,000
    (b) Rs. 5,000
    (c) Rs. 4,700
    (d) Rs. 5,500
    (e) Rs. 7,580

 

Answer Option :1

Solution »
SI at the rate of 4% for 2 years ,
=( P* 4*2)/100 = 8P/100
SI at the rate of 6% for 4 years ,
(P*6*4)/100 = 24P/100
SI for the next 3 years
SI = (P*8*3)/100 = 24P/100
Total SI = 8P/100 + 24P/100 + 24P/100
=>P = (1680*100 )/56 = 3000

 

13. The rates of simple interest in two banks A and B are in the ratio 5 : 4. A person wants to deposit his total savings in two banks in such a way that he receives equal half-yearly interest from both. He should deposit the savings in banks A and B in the ratio

(a) 2:5
(b) 4 :5

(c) 5:2

(d) 5:4

(e) None of these

 

Answer Option :2

Solution »

 

14. The rate of interest on a sum of money is 4% per annum for the first 2 years, 6% per annum for the next 4 years and 8% per annum for the period beyond 6 years. If the simple interest accrued by the sum for a total period of 9 years is Rs. 1,120, then the sum is
    (a) Rs. 2,400

(b) Rs. 2,200
(c) Rs. 2,000

(d) None of these.

 

Answer Option :3

Solution »

 

15. A person invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested, he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest?

(a) Rs. 700

(b) Rs. 800

(c) Rs. 500

(d) Rs. 400

(e) None of these

 

Answer Option :3

Solution »