Question

In a week, P and Q earn money in the ratio 5 : 4 and their expenses are in the ratio 2 : 1. If they save each Rs. 3000 in the week, then in the week, the incomes of P and Q are (in Rs)

• A. 10000, 8000
• B. 5000, 4000
• C. 8000, 6000
• D. 8000, 7000

Answer 1

The Correct Option is B

Let the incomes of P and Q be \( 5x \) and \( 4x \) respectively. Their expenses are in the ratio 2 : 1, so the expenses of P and Q are \( 2y \) and \( y \) respectively. The savings for P and Q are:
\[ \text{Savings of P} = 5x - 2y = 3000 \quad \text{and} \quad \text{Savings of Q} = 4x - y = 3000 \]

Solve the system of equations:
\[ 5x - 2y = 3000 \quad (1) \]
\[ 4x - y = 3000 \quad (2) \]

From equation (2), \( y = 4x - 3000 \), substitute into equation (1):
\[ 5x - 2(4x - 3000) = 3000 \]
\[ 5x - 8x + 6000 = 3000 \quad \Rightarrow \quad -3x = -3000 \quad \Rightarrow \quad x = 1000 \]

The incomes are \( 5x = 5000 \) and \( 4x = 4000 \).

To solve for unknowns in a system of equations, substitute values from one equation into the other and solve step by step.