Question

Divide ₹ 10000 in two parts so that the simple interest on the first part for 4 years at 12 per cent per annum may be equal to the simple interest on the second part for 4.5 years at 16 per cent per annum.

Answer 1

Given, money = ₹ 10000

Now, we have divide ₹ 10000 in two parts such that SI on first part for 4 years at 12% per annum may be equal to the SI on second part for 4.5 years at 16%.

Let first part = 7x

Then, second part = ₹ (10000 – x)

For first part, we have P₁ = ₹ x, T₁ = 4 years and R₁ = 12%

∴ `SI_1 = (P_1 xx R_1 xx T_1)/100 = (x xx 12 xx 4)/100`

For second part (10000 – x), we have

P₂ = ₹ (10000 – x), T₂ = 4.5 years and R₂ = 16%

∴ `SI_2 = (P_2 xx R_2 xx T_2)/100 = ((10000 - x) xx 16 xx 4.5)/100`

Since, SI₁ is equal to SI₂

Then, according to the question,

`(x xx 12 xx 4)/100 = ((10000 - x) xx 16 xx 4.5)/100`

⇒ 48x = (10000 – x) × 16 × 4.5

⇒ `(48x)/(4.5 xx 16) = (10000 - x)`

⇒ `(48x xx 10)/(45 xx 16) = 10000 - x`

⇒ `2/3x = 10000 - x`

⇒ `2/3x + x = 10000`

⇒ `(5x)/3 = 10000`

⇒ `x = 10000 xx 3/5 = 6000`

First part = x = ₹ 6000 

Second part = 10000 – x = 10000 – 6000 = ₹ 4000

Hence, two parts of the sum are ₹ 6000 and ₹ 4000.