Question

If $50 amounts to $70 in 4 years at some rate of simple interest per annum, how much will $160 become in 5 years at the same rate of interest?​

Answer 1

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Answer 2

Given :

Principle : $50

Total Amount : $70

Time : 4 years

To find :

The interest if the principle and time is $160 and 5 years at same rate of interest.

Solution :

First, we should find the simple interest of first case

Simple interest :

$\sf \dashrightarrow Total \: Amount - Principle$

$\sf \dashrightarrow 70 - 50$

$\sf \dashrightarrow 20$

Now, we can find the rate of interest.

Rate of interest :

$\sf \dashrightarrow SI = \dfrac{P \times R \times T}{100}$

$\sf \dashrightarrow 20 = \dfrac{50 \times R \times 4}{100}$

$\sf \dashrightarrow 20 = \dfrac{200 \times R}{100}$

$\sf \dashrightarrow R = \dfrac{20 \times 100}{200}$

$\sf \dashrightarrow R = \dfrac{1 \times 100}{10}$

$\sf \dashrightarrow R = \dfrac{100}{10}$

$\sf \dashrightarrow R = 10\%$

Now, we can find the simple interest at second case

Simple interest (2) :

$\sf \dashrightarrow SI = \dfrac{P \times R \times T}{100}$

$\sf \dashrightarrow \dfrac{160 \times 10 \times 5}{100}$

$\sf \dashrightarrow \dfrac{8 \times 10 \times 5}{5}$

$\sf \dashrightarrow \dfrac{40 \times 10}{5} = \dfrac{400}{5}$

$\sf \dashrightarrow \cancel \dfrac{400}{5} = 80$

Now, we can find the total amount.

Total Amount :

$\sf \dashrightarrow Simple \: Interest + Principle$

$\sf \dashrightarrow 80 + 160$

$\sf \dashrightarrow Rs.240$

Hence, the amount at second case is $240.