Question
5 carpenters and 3 painters earn Rs. 4,000 in 5 days. 8
carpenters and 4 painters earn Rs. 7,200 in 6 days. What will 6 carpenters and 2 painters earn in 4 days?Solution
ATQ,
Let carpenter earns x/day, painter earns y/day
5x + 3y = 4000 / 5 = 800 ……… (i)
8x + 4y = 7200 / 6 = 1200 ……… (ii)
Multiply (i) by 4: 20x + 12y = 3200
Multiply (ii) by 3: 24x + 12y = 3600
Subtract: 4x = 400 ⇒ x = 100
Put in (i): 5×100 + 3y = 800 ⇒ 500 + 3y = 800 ⇒ y = 100
Now, earnings of 6 carpenters and 2 painters in 4 days:
= (6×100 + 2×100) × 4 = (600 + 200) × 4 = 800 × 4 = Rs. 3,200
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