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- 16. A sum is invested at compounded interest payable annually. The interest in the first two successive years was Rs. 400 and Rs. 420. The sum is
A.Rs. 8000
B.Rs. 8200
C.Rs.7500
D.Rs. 8500
Answer & Explanation
Answer: Option A 
his means that, simple Interest on Rs.400 for 1 year = 420 - 400 = 20
Rate = (100 ×SI)/PT = (100 × 20)/(400×1) = 5%
Rs.400 is the interest on the sum for 1st year
Hence, sum = (100 × SI)/RT = (100 × 400)/(5 × 1) = Rs. 8000
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- 17. Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.
A.20%
B.10%
C.40%
D.50%
Answer & Explanation
Answer: Option C
Let the sum be x
Simple interest on x for 2 years = Rs.2000
Simple interest = PRT/100
2000 = x × R × 2100
⇒ xR = 100000 --- (1)
Compound Interest on x for 2 years = 2400
P(1+R/100)T−P=2400
x(1+R/100)2 − x = 2400
x(1+2R/100 + R2/10000) − x = 2400
x(2R/100 + R2/10000) = 2400
2xR/100 + xR2/10000 = 2400 --- (2)
Substituting the value of xR from (1) in (2) ,we get
(2 × 100000)/100 + (100000×R)/10000 = 2400
2000 + 10R = 2400
10R = 400R = 40%
View Answer
- 18. If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:
A.12 years
B.18 years
C.16 years
D.14 years
Answer & Explanation
Answer: Option C
Let the sum be P
The sum P becomes 3P in 4 years on compound interest
3P = P(1+R/100)4
⇒ 3 = (1+R/100)4
Let the sum P becomes 81P in n years
81P = P(1+R/100)n
⇒ 81 = (1+R/100)n
⇒ (3)4 =(1+R/100)n
⇒((1+R/100)n)n
=(1+R/100)n
⇒ (1+R/100)16
= (1+R/100)n
n = 16
i.e, the sum will become 81 times in 16 years
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- 19. The difference between the simple interest on a certain sum at the rate off 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs. 124.05. What is the principal sum?
A.Rs. 6000
B.Rs. 8000
C.Rs. 12000
D.Rs. 10000
Answer & Explanation
Answer: Option B
Let the sum be P
Compound Interest on P at 10% for 2 years when interest is compounded half-yearly
=P(1+(R/2)/100)2T − P = P(1+(10/2)/100)2×2 − P = P(1+1/20)4 − P = P(21/20)4 − P
Simple Interest on P at 10% for 2 years = PRT/100 = (P × 10 × 2)/100 = P/5
Given that difference between compound interest and simple interest = 124.05
=> P(21/20)4 − P − P/5 = 124.05
=> P[(21/20)4 − 1 − 15] = 124.05
=> P[(194481 − 160000 − 32000)/160000] = 124.05
=> P[2481/160000] = 124.05
=> P = (124.05 × 160000)/2481 = 160000/20 = 8000
View Answer
- 20. A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
A.10 years
B.8 years
C.6 years
D.12 years
Answer & Explanation
Answer: Option D
Let the sum be Rs.1 which becomes Rs.2 after 4 years
⇒ 2 = 1(1 + R/100 )4 --- (equation 1)
Let the sum of Rs.1 becomes Rs.8 after n years
⇒ 8 = 1(1 + R/100)n --- (equation 2)
⇒ (2)3 = 1(1+R/100)n
⇒ [1(1+R/100)4]3 = 1(1+R/100)n (∵ replaced 2 with the value in equation 1) (1 + R/100)12 = (1+R/100)n
⇒ n = 12
i.e., the sum amounts to 8 times in 12 years
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