Question

A man borrowed Rs.X at a simple interest of 35% per annum for 6 years and Rs.Y at a simple interest of 20% per annum for 6 years. If he had borrowed Rs. (X + Y) at a simple interest of 25% for 6 years, he would have paid the same interest. Find the ratio of X and Y.
1. 2 : 3
2. 1 : 2
3. 3 : 4
4. 3 : 5
5. 2 : 5

Answer 1

Correct Answer - Option 2 : 1 : 2

Given:

A man borrowed Rs.X at a simple interest of 35% per annum for 6 years.

A man borrowed Rs.Y at a simple interest of 20% per annum for 6 years.

Formula Used:

Simple interest = (Principal × Rate × Time)/100

Calculation:

A man borrowed Rs.X at a simple interest of 35% per annum for 6 years.

Simple interest on Rs. X = (X × 35 × 6)/100 = 21X/10

A man borrowed Rs.Y at a simple interest of 20% per annum for 6 years.

Simple interest on Rs. Y = (Y × 20 × 6)/100 = 12Y/10

According to the question:

A man borrowed  Rs. (X + Y) at a simple interest of 25% for 6 years

Simple interest on Rs. (X + Y) = [(X + Y) × 25 × 6]/100 = (15/10)(X + Y)

Then, the simple interest paid is equal,

⇒ 21X/10 + 12Y/10 = (15/10)(X + Y)

⇒ 21X/10 - 15X/10 = 15Y/10 - 12Y/10

⇒ 6X/10 = 3Y/10

⇒  X ∶ Y = 1 ∶ 2

∴ The ratio of X and Y is 1 : 2.