Question

If Rs.640 amounts to Rs.768 in 2 years 6 months, what will Rs.850 amount to in 3 years at the same rate percent per annum?

Answer 1

Hint: In this problem, we are given that in 2 years 6 months Rs. 640 amounts to 768, we have to find the amount present in 3 years, whose principal amount is Rs.850 at the same rate. Here we can first find the rate at which Rs.640 amounts to 768 in 2 years 6 month using the formula $$Rate={\displaystyle \frac{S.I\times 100}{P\times T}}$$. We can then find the amount increased from Rs. 850 at the same rate at 3 years, using the same formula.

Complete step by step answer:
Here we are given that in 2 years 6 month Rs. 640 amounts to 768 and we have to find the amount increased from Rs. 850 at the same rate at 3 years.
We can now find the rate for the given Principal amount, P = Rs.640, Time, T = 2 years 6 month.
Simple interest = A – P
$$\Rightarrow S.I=768-640=128$$
We know that,
$$Rate={\displaystyle \frac{S.I\times 100}{P\times T}}$$
We can now substitute the above values in the above formula, we get
$$\Rightarrow Rate={\displaystyle \frac{128\times 100}{640\times 2.5}}={\displaystyle \frac{128\times 40}{640}}=8\mathrm{\%}$$
The rate is $$8\mathrm{\%}$$.
We can now find the amount increased from Rs. 850 at the same rate at 3 years.
Where Principle amount, P = Rs.850, Rate, R = $$8\mathrm{\%}$$, Time, T = 3 years.
We can now substitute these values in $$S.I={\displaystyle \frac{P\times R\times Time}{100}}$$, we get
$$\Rightarrow S.I={\displaystyle \frac{850\times 8\times 3}{100}}=204$$
We know that,
Amount = Principal amount + Simple interest
Amount = 850 + 204 = Rs.1054
Therefore, the required amount is Rs.1054.

Note: We should always remember that the initial amount deposited is Principle and the simple interest is equal to the difference of the present amount and the principle amount. We should also remember the formula $$Rate={\displaystyle \frac{S.I\times 100}{P\times T}}$$, to find the required answer for the given problem.