Question

₹ 4000 amount to ₹ 5000 in 8 years. In what time will ₹ 1600 amount to ₹ 2400 at the same rate?

• A. 12 years
• B. 10 years
• C. 16 years
• D. 20 years

Answer 1

The correct option is C

16 years

Principal (P) = ₹ 4000 ; Amount = ₹ 5000

Hence Interest (I) = ₹ 5000 - ₹ 4000 = ₹ 1000
Let the rate per annum be 'R'
Time (n)= 8 years

Now, $I=\frac{PTR}{100}$

$⟹$1000 = $\frac{4000\times 8\times R}{100}$

$R=\frac{25}{8}$ %
In the second case P = 1600 and Amount = ₹ 2400

Hence I = ₹ 2400 - ₹ 1600 = ₹ 800

Let the time be n and rate of interest = $\frac{25}{8}$ %

Then, 800 = $\frac{1600\times 25\times n}{100\times 8}$

$⟹$ n = $\frac{800\times 8\times 100}{1600\times 25}$

Therefore n = 16 years