Question

Koushal, Abhilash and Nikhila jointly started a business. Koushal invested $\frac{1}{4}th$ of the total capital. Abhilash invested $\frac{1}{4}th$ of the total capital. Nikhila invested the remaining part of the capital. If the total profit is ₹ 2400 at the end of the year, find the profit earned by each of them .

• A. Koushal's Profit is Rs. 600
  Abhilash's Profit is Rs. 600
  Nikhila's Profit is Rs. 1200
• B. Koushal's Profit is Rs. 700
  Abhilash's Profit is Rs. 600
  Nikhila's Profit is Rs. 1200
• C. Koushal's Profit is Rs. 600
  Abhilash's Profit is Rs. 800
  Nikhila's Profit is Rs. 1300
• D. Koushal's Profit is Rs. 500
  Abhilash's Profit is Rs. 600
  Nikhila's Profit is Rs. 700

Answer 1

The correct option is A

Koushal's Profit is Rs. 600
Abhilash's Profit is Rs. 600
Nikhila's Profit is Rs. 1200

Let the total capital invested be ₹ z.
Koushal invested $\frac{1}{4}th$ of the total capital, so Koushal's investment = $\frac{z}{4}$
Abhilash invested $\frac{1}{4}th$ of the capital, so Abhilash's investment = $\frac{z}{4}$
Nikhila invested the remaining part of the capital, hence:

Nikhila's investment = Total Capital - Koushal's investment - Abhilash's investment
$\Rightarrow$ $z$ - $\frac{z}{4}$ - $\frac{z}{4}$
$\Rightarrow$ $z$ - $\frac{2z}{4}$
$\Rightarrow$ $z$ - $\frac{z}{2}$
$\Rightarrow$ $\frac{z}{2}$

Capital of Koushal : Capital of Abhilash : Capital of Nikhila = $\frac{z}{4}$ : $\frac{z}{4}$ : $\frac{z}{2}$

$\Rightarrow$ $\frac{1}{4}$ : $\frac{1}{4}$ : $\frac{1}{2}$
$\Rightarrow$ 1 : 1 : 2

Koushal's profit = $2400\times \frac{1}{4}$ = ₹ 600

Abhilash's profit = $2400\times \frac{1}{4}$ = ₹ 600

Nikhila's profit = $2400\times \frac{1}{2}$ = ₹ 1200