Simple Interest and Compound Interest Problems and Solutions
Problems with Solutions of Simple and Compound Interest
Q.6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) None of these
Ans . D
S.I. = Rs. (15500 ⎯ 12500) = Rs.3000
Rate = [ (100 × 3000) / (12500 × 4) ]% = 6%
Q.7. A sum of Rs. 1000 is to be divided among two brothers such that if the interest being compounded annually is 5 % per annum, then the money with the first brother after 4 years is equal to the money with the second brother after 6 years.
(A) 425 and 498
(B) 400 and 489
(C) 500 and 575
(D) 524.38 and 475.62
(E) None of these
Ans . D
Let the first brother be given Rs. P
→ Money with second brother = Rs. 1000 – P
Now, according to the question,
P [1 + (5 / 100)]4 = (1000 – P) [1 + (5 / 100)]6
→P (1.05)4 = (1000 – P) (1.05)6
→ 0.9070 P = 1000 – P
→ 1.9070 P = 1000
→ P = 524.38
Therefore, share of first brother = Rs. 524.38
Share of second brother = Rs. 475.62
Q.8. Aastha lent Rs. 5000 to Bahubali for 2 years and Rs. 3000 to Chinky for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
(A) 5%
(B) 7%
(C) 7 1/8%
(D) 10%
(E) None of these
Ans . D
Let the rate be R% p.a.
Then, [ 500 × R × 2 / 100 ] + [300 × R × 4 / 100] = 2200
100R + 120R = 2200
R = [2200 / 220] = 10
So, rate = 10%
Q.9. A sum of Rs. 1000 was lent to two people, one at the rate of 5 % and other at the rate of 8 %. If the simple interest after one year is Rs. 62, find the sum lent at each rate.
(A) 400, 600
(B) 800, 1200
(C) 300, 500
(D) 700, 900
(E) None of these
Ans . A
Let the sum lent at 5 % be P.
→ Sum lent at 8 % = 1000 – P
Now, according to the question,
SI for 5 % + SI for 8 % = 62
→ (P x 5 x 1 / 100) + ((1000 – P) x 8 x 1 / 100) =62
→ 5 P + 8 (1000 – P) = 6200
→ 5 P + 8000 – 8 P = 6200
→ 3 P = 1800
→ P = 600
Therefore, sum lent at 5 % = P = Rs. 600
Sum lent at 8 % = 1000 – P = Rs. 400
Q.10. Find the compound interest on Rs. 3000 at 5% for 2 years, compounded annually.
(A) 307.5
(B) 3307.5
(C) 3000.5
(D) 3100
Ans . A
Amount with CI = 3000 (1+ 5/100)2 = Rs. 3307.5
Therefore, CI = 3307.5 – 3000 = Rs. 307.5
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