Single correct option
The monthly incomes of two employees P and Q are in the ratio 4 : 3 and their monthly expenditures are in the ratio 2 : 1. If each of them saves Rs 1,800 per month, what is P's monthly income?
- A. Rs 2,700
- B. Rs 3,200
- C. Rs 3,600
- D. Rs 4,500
Show answer and solution
Answer: (C) Rs 3,600
Let incomes be 4x and 3x, expenditures 2y and y.
4x − 2y = 1800 … (i)
3x − y = 1800 … (ii)
From (ii), y = 3x − 1800. Substituting in (i): 4x − 2(3x − 1800) = 1800 ⇒ 4x − 6x + 3600 = 1800 ⇒ −2x = −1800 ⇒ x = 900.
P's income = 4 × 900 = Rs 3,600 (Q's income = 2,700; expenditures 1,800 and 900, ratio 2:1 ✓, both save 1,800 ✓).
Tip: with two linear equations in x and y, eliminate one variable using substitution — plugging in the answer options directly also verifies quickly.
4x − 2y = 1800 … (i)
3x − y = 1800 … (ii)
From (ii), y = 3x − 1800. Substituting in (i): 4x − 2(3x − 1800) = 1800 ⇒ 4x − 6x + 3600 = 1800 ⇒ −2x = −1800 ⇒ x = 900.
P's income = 4 × 900 = Rs 3,600 (Q's income = 2,700; expenditures 1,800 and 900, ratio 2:1 ✓, both save 1,800 ✓).
Tip: with two linear equations in x and y, eliminate one variable using substitution — plugging in the answer options directly also verifies quickly.
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