Simple Interest - Aptitude Questions and Answers Part 2

6. If I invest Rs 3000 at a simple interest for 4 years, I earn a certain amount. However, if I invest Rs 3500 at the same rate, for the same duration, I would earn Rs 130/- more. Find the rate of interest.

a. 6.5%
b. 10.50%
c. 12%
d. 13%

Answer: a. 6.5%

Explanation:

Let Simple Interest be S
∴ S2 - S1 = Rs. 130

Simple Interest =PRT
100
∴P2 x R2 x T2-P1 x R1 x T1= 130  
100100
∴3500 x R x 4-3000 x R x 4= 130
100100

∴ 140R - 120R = 130
∴ R = 6.5%


7. A small broker lends his money in parts to some farmers in the village at simple interest.  He lends the money as follow and earns an interest of Rs 297 at the end. Find the amount he lends.

AmountRate of interest
1/5 part of the amount3%
1/3 part5%
2/5 parts9%
Remaining amount11%

a. 3950
b. 4200
c. 4500
d. 5500

Answer: c. 4500

Explanation:

Original amount = P
Consider time T = 1 year

Parts of amounts are1,1,2and remaining amount
535
Remaining amount = 1 - (1+1+2)
535
Make denominators common. We have 5, 3 and 5 in denominators.
5 x 3 = 15
∴ Remaining Amount = 1- (1 x 3+1 x 5+2 x 3) = 1- (3+5+6) = 1-14=1
5 x 33 x 55 x 31515151515
Simple interest for all parts = Rs. 297

∴P/5  x 3 x 1+P/3  x 5 x 1+2P/5  x 9 x 1+P/15  x 11 x 1= 297
100100100100
∴3P+5P+18P+11P= 297 x 100
53515
Making denominators common.
∴9P+25P+18P+11P= 297 x 100
15151515
∴ P= 4500


8. Rohit lends his 40800 Rs in two parts at simple interest. He lends one part for a period of 8 years at a rate of 6.25%. The other part he lends for 5 years at a rate of 7%. Both the parts earn him the same interest. Find the value of the smaller part of money.

a. 1300
b. 16800
c. 19200
d. 20100

Answer: b. 16800

Explanation:

Two parts are = A and (40800 - A)
Time period and Simple interest are same for both

Simple Interest =PRT
100
∴A x 6.25 x 8=(40800-A)  x 7 x 5
100100
∴ 50A = 35 x 40800 - 35A
∴ 85A = 35 x 40800
∴ A = 8400
Smaller amount is Rs. 16800
By direct observation we can say that 16800 is smaller - as it is smaller than half of 40800.


9. Mr. Sharma has a debt of Rs. 1078/- which he wants to completely pay off in 6 years. The rate of interest he is charged is 9% pa. Find the value of his yearly installments.

a. Rs.118.35
b. Rs.126.55
c. Rs.146.35
b. Rs.156.25

Answer: c. Rs.146.35

Explanation:

First take Installment amount = P = Rs. 100
Total installments = 6 (One installment per year)

Simple and Easy rule -
If there are 'n' installments, then, 1st installment will have interest for (n-1) years, 2nd will have interest for (n-2) years and so on.


So in this case, n=6
∴ 1st installment will have interest for 5 years (n-1 = 6-1=5 years)
2nd installment will have interest for 4 years (n-2 = 6-2=4 years)
3rd installment will have interest for 3 years (n-3 = 6-3= 3 years)
4th installment will have interest for 2 years (n-4 = 6-4= 2 years)
5th installment will have interest for 1 year (n-5 = 6-5= 1 year)
6th installment will have no interest (n-6 = 6-6= 0 years)

Total Amount = 6 Installments + Interest on those 6 Installments
∴ Total Amount = (6 x 100) +P x R x T
100

Now here, rate of interest is same for all installments = R = 9%
P = Rs. 100        (same amount Rs. 100 for all installments)
From above rule we can calculate effective time period 'T'
T (for interest calculation) = 5 years + 4 years + years + 2 years + 1 year + 0 years
∴ T = 15 years
∴ Total Amount = 600 +100 x 9 x 15= 600+ 135 = 735
100
For installment of Rs. 100 : Total Amount = Rs. 735

For ? installment : Total Amount is Rs. 1078
∴ 1078 x 100 = 735 x ?
∴ ? =1078 x 100= Rs.146.35
735


10. Anuj has some extra money which he decides to lend on interest. He lends 40% of the money at a rate of 15% p.a., half of the remaining money at 10% pa and all the money left at 18% p.a. If the interest was calculated on the complete amount he lent, find the rate of interest.

a. 13.4% p.a.
b. 13.33% p.a.
c. 14.4% p.a.
d. 14.33% p.a.

Answer: c. 14.4% p.a.

▲