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A certain sum of money amounts to Rs. 1680 in 3 years and to 1800 in 5 years. Find the sum and the rate of interest.
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- 1500; 4%
- 1200; 4%
- 1600; 5%
- 1800; 5%
Correct Option: A
We know that , Amount = Principal + SI
So,P remains same in both cases. Only amount of interest is different in two cases because the time period are different.
P + Interest for 5 years = ₹ 1800 and P + Interest for 3 years = ₹ 1680
On subtraction we get,
Interest for 2 years = ₹ 120
Now, we solve for the case of 3 years.
Interest for 3 years
| ₹ 120 × | = ₹ 180 | |
| 2 |
And amount after 3 years = 1680
Principal (P) = Amount – SI = ₹ (1680 – 180) = ₹ 1500.
| Rate = | |
| Principal × Time |
| R = | |
| 1500 × 3 |
⇒ R = 4%.
Note : Alternatively, we could have solved for 5 years too and got the same answer.
