Simple Interest problems
- 1. A sum of money amounts to ? 2240 at 4% per annum simple interest in 3 yr. The interest on the same sum for 6 months at 3.5% per annum is
Options- A. ? 30
- B. ? 50
- C. ? 35
- D. ? 150 Discuss
Correct Answer: ? 35
Explanation:
If the sum be ? P, then
(2240 - P) = (P x 4 x 3)/100
? 2240 = 12P/100 + P
? 2240 = 112P/100
? P = (2240 x 100)/112 = ? 2000
Now, required interest,
SI = PRT/100 = [{2000 x (7/2) x (1/2)} /100]
= ? 35
- 2. The simple interest on a sum of money at 9% per annum for 5 yr is half the sum. What is the sum?
Options- A. ? 5800
- B. ? 5000
- C. ? 7000
- D. Data is inadequate Discuss
Correct Answer: Data is inadequate
Explanation:
Let the sum be P.
? SI = P/2
? P/2 = (P x 9 x 5)/100
Clearly data is inadequate.
- 3. The simple interest on a sum of money at 8% per annum for 6 yr is half the sum. What is the sum?
Options- A. ? 4800
- B. ? 6000
- C. ? 8000
- D. Data is inadequate Discuss
Correct Answer: Data is inadequate
Explanation:
Let sum = P
Then, according to the question.
SI = P/2
? P/2 = (P x 8 x 6)/100
? It is clear that data is inadequate.
- 4. A sum was put at simple interest at a certain rate for 2 years . Had it been put at 3% higher rate, it would have fetched Rs 300 more. The sum is
Options- A. Rs 5000
- B. Rs 6000
- C. RS 7000
- D. None Of these Discuss
Correct Answer: Rs 5000
Explanation:
Let the sum be P.
And the original rate be y% per annum.
Then new rate=(y+3)% per annum
According to question, [(P × (y+3) × 2)/100]=[(P × y × 2)/100]=300
? [(Py + 3P)/100]=[Py/100] = 150
? Py+ 3P - Py=15000
? 3P=15000
? P= 5000
Thus, the sum is Rs 5000
- 5. The simple interest on a sum of money at 10% per annum for 6 year is half the sum. Then, the sum is?
Options- A. Rs 5000
- B. Not possible
- C. Rs 4000
- D. Rs 6000 Discuss
Correct Answer: Not possible
Explanation:
Let the sum be Rs 'y'
Since Simple Interest = Rs ( y / 2)
and, T = 6 yr , R = 10% per annum
So Simple Interest, SI = (P x R x T)/100
where, R = Rate
T = Time
SI= Simple Interest
now, According to problem, ( y / 2 ) = ( y x 10 x 6)/100
? (1/2)=(6/10)
? which is not true, so it is not a possible case.
- 6. The simple interest at x% for x years will be Rs x on a sum of ....
Options- A. Rs x
- B. Rs 100x
- C. Rs (100/x)
- D. Rs (100/ x2) Discuss
Correct Answer: Rs (100/x)
Explanation:
As Sum = [(100 x SI)/(Time x Rate)]
here, let R =x%, T=x yr, and, SI=Rs x
? Sum=[(100 × x)/(x × x)]
=(100/x)
- 7. A certain sum lent out at simple interest amounts to Rs 575 in 3 yr and to Rs 625 in 5 yr. Then the rate of interest is?
Options- A. 3%
- B. 4%
- C. 5%
- D. 7% Discuss
Correct Answer: 4%
Explanation:
Let the sum be Rs 'y' and , rate of interest = R%
Simple Interest for 2 yr =Rs( 625 - 575 ) = Rs 50
? Sum of money, y=Rs( 575 - 75)= Rs 500
? R= [(100 x SI)/(Sum x Time)]
=[(100x 75)/(500 x 3)]=5 %
- 8. The simple interest on a sum of money is 1/9 of the principle and the number of years is equal to the rate percent annum. The rate percent annum is?
Options- A. 3
- B. 1/3
- C. 31/3
- D. 3/10 Discuss
Correct Answer: 31/3
Explanation:
Let principle = Rs. P
Then S.I = P/9
Let Rate = R% per annum and time = R years
Then, as we know SI = (P x R x T) / 100.
? P/9 = ( P x R x R) / 100
? R2 = 100/9
? R = 10/3 = 31/3 % per annum
- 9. A moneylender finds that due to a fall in the rate of interest from 13% to 12 1/ 2% his yearly income diminishes by Rs. 104. His capital is?
Options- A. Rs. 21400
- B. Rs. 20800
- C. Rs. 22300
- D. Rs. 24000 Discuss
Correct Answer: Rs. 20800
Explanation:
Let capital = Rs . P
Then, SI1 - SI2 = 104.
? (P x 13 x 1)/100 - (P x 25/2 x 1) /100 = 104
? 13P/100 - P/8 = 104
? 26P -25P = (104 x 200)
? P = 20800
? Capital = Rs. 20800
- 10. A man invested 1/3 of his capital at 7%, 1/4 at 8% and remainder at 10%. If his annual income is Rs. 561, the capital is?
Options- A. Rs. 5400
- B. Rs. 6000
- C. Rs. 6600
- D. Rs. 7200 Discuss
Correct Answer: Rs. 6600
Explanation:
Let the capital be Rs. P, then
(P/3) x (7/ 100) + (x/4) x (8/100) + [P - (P/3 + P/4)] x 10/100 = 561
? 7P/300 + P/50 + P/24 = 561
? 42P + 36P + 75P = 1009800
P = 1009800/153 = 6600
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