Simple Interest problems
- 1. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
Options- A. 3.6%
- B. 4.5%
- C. 5%
- D. 6%
- E. None of these Discuss
Correct Answer: None of these
Explanation:
Let the original rate be R%. Then, new rate = (2R)%.
Note:
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. ⅓ year(s).
| ∴ | ❨ | 725 x R x 1 | ❩ | + | ❨ | 362.50 x 2R x 1 | ❩ | = 33.50 |
| 100 | 100 x 3 |
⟹ (2175 + 725) R = 33.50 x 100 x 3
⟹ (2175 + 725) R = 10050
⟹ (2900)R = 10050
| ⟹ R = | 10050 | = 3.46 |
| 2900 |
∴ Original rate = 3.46%
- 2. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Options- A. Rs. 35
- B. Rs. 245
- C. Rs. 350
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: Cannot be determined
Explanation:
We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate.
- 3. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6¼% p.a for 2 years. Find his gain in the transaction per year.
Options- A. Rs. 112.50
- B. Rs. 125
- C. Rs. 225
- D. Rs. 167.50 Discuss
Correct Answer: Rs. 112.50
Explanation:
| Gain in 2 years |
|
||||||||||||||||
| = Rs. (625 - 400) | |||||||||||||||||
| = Rs. 225. |
| ∴ Gain in 1 year = Rs. | ❨ | 225 | ❩ | = Rs. 112.50 |
| 2 |
- 4. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
Options- A. 1 : 3
- B. 1 : 4
- C. 2 : 3
- D. Data inadequate
- E. None of these Discuss
Correct Answer: 2 : 3
Explanation:
Let the principal be P and rate of interest be R%.
| ∴ Required ratio = |
|
= | 6PR | = | 6 | = 2 : 3. | ||||
|
9PR | 9 |
- 5. The sum required to earn a monthly interest of Rs 400 at 10 % per annum at simple interest is
Options- A. Rs 2000
- B. Rs 12000
- C. Rs 24000
- D. Rs 48000 Discuss
Correct Answer: Rs 48000
Explanation:
Total interest needed in a year = Rs 400 × 12
= Rs 4800
Principal = (100 × SI)/R × T
where, R = Rate
T = Time
SI= Simple Interest
- 6. In what time will the simple interest on Rs 400 at 10% per annum be the same as the simple interest on Rs 1000 for 4 year at 4 % per annum?
Options- A. 2 yrs
- B. 3 yrs
- C. 4 yrs
- D. 6 yrs Discuss
Correct Answer: 4 yrs
Explanation:
Here , P= Rs 1000
T= 4 yrs
R= 4 %
where, P= Principal
T= Time
R= Rate
Since , Simple Interest on Rs 1000=(1000 × 4 × 4)/100
= Rs 160
now, simple interest=Rs 160
P = Rs 400
R = 10 %
then, T=(100 × SI)/P × R
= (100 × 160)/(400 × 10)
= 4 yr
- 7. At what rate percent per annum will a sum of money double in 8 yr?
Options- A. 12 %
- B. 12.5 %
- C. 13 %
- D. 15 % Discuss
Correct Answer: 12.5 %
Explanation:
Let Sum = P, Then SI=P
As Amount A = 2 × P
where , P = Principal
Rate R = (100 × SI)/(P × T)
= (100 × P)/(P × 8) %
= 12.5 %
where , SI= Simple Interest
T= Time
- 8. The amount instalment will discharge on debit of Rs 3220 due in 4 year at 10 % simple interest?
Options- A. 500
- B. 600
- C. 700
- D. None of these Discuss
Correct Answer: 700
Explanation:
Let the amount instalment be Rs ' x '
Then According to question,
(Amount of 'x' for 3 yrs) + (Amount of 'x' for 2 yrs) + (Amount of 'x' for 1 yrs) + x =3220
or, [x+(x × 10 × 3)/100] + [x+(x × 10 × 2)/100] + [x+(x × 10 × 1)/100] + x=3220
? 4x+ (30x/100)+(20x/100)+(10x/100)=3220
? 460x=322000
? x=Rs 700
? Each Instalment= Rs 700
- 9. A certain sum amounts to Rs 1586 in 2 year and Rs 1729 in 3 year. Find the rate and the sum.
Options- A. 8 %
- B. 9 %
- C. 10 %
- D. 11 % Discuss
Correct Answer: 11 %
Explanation:
Simple Interest in 1 year= Rs (1729 - 1586)
= Rs 143
now, SI in 2 year = Rs 286
Principal P= Rs(1586 - 286)
= 1300
And R= (100 × SI)/(P × T)
= (100 × 143)/(1300 × 1)
= 11 %
where, R = rate
SI= Simple Interest
P = Principal
T= Time
- 10. Find the sum of money will amount to Rs 900 in 4 years at 5 % per annum on simple interest?
Options- A. Rs 750
- B. Rs 650
- C. Rs 500
- D. Rs 550 Discuss
Correct Answer: Rs 750
Explanation:
Let the sum of money be Rs y
So Amount = y +[( y x 5 x 4 )/100]
But Amount = Rs 900
? 900 = y +(20y)/100
? 900 = 6y / 5
? y = ( 900 x 5) /6
= Rs 750
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