A certain sum of money amounts to Rs. 6600 in 4 years at a certain rate percent simple interest. If the rate of interest be increased by its 25%, the same sum would amount to Rs. 7000 during the same period. Find the sum.

Question

Question

This question was previously asked in

NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper

Answer 1

Given:

Amount (A₁) = ₹6600

Amount (A₂) = ₹7000

Time (t) = 4 years

New Rate = r + 25% of r = r + (r × 25/100) = 1.25r

Formula used:

Simple Interest (SI) =

Amount = Principal + SI

Calculation:

Let P = x, r = R

A₁ = x + = 6600

⇒ x(1 + ) = 6600

⇒ x(1 + ) = 6600. —(1)

A₂ = x + = 7000

⇒ x(1 + ) = 7000

⇒ x(1 + ) = 7000 —(2)

Divide (2) by (1):

⇒

Let’s simplify:

⇒

⇒ Cross multiply:

33(500 + 25R) = 35(500 + 20R)

⇒ 16500 + 825R = 17500 + 700R

⇒ 825R - 700R = 17500 - 16500

⇒ 125R = 1000

⇒ R = 8%

Now put R in eq (1):

x(1 + ) = 6600

⇒ x × = 6600

⇒ x =

∴ The correct answer is ₹5000.

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