Question
Selling price of a cap is at 10% profit, and that of a
scarf is 25%. If total profit on selling 6 caps and 3 scarves is Rs. 48, and on selling 4 caps and 5 scarves is Rs. 65, what is the cost price of a cap?Solution
ATQ,
Let CP of cap = 100x, scarf = 100y
SP of cap = 110x, scarf = 125y
Profit:
6(110x) + 3(125y) – 6(100x) – 3(100y) = 48
⇒ 60x + 75y = 48 ……… (1)
4(110x) + 5(125y) – 4(100x) – 5(100y) = 65
⇒ 40x + 125y = 65 ……… (2)
(1) × 2 → 120x + 150y = 96
(2) × 3 → 120x + 375y = 195
Subtract:
-225y = -99 ⇒ y = 0.44
Put in (1):
60x + 75 × 0.44 = 48
⇒ 60x + 33 = 48 ⇒ x = 0.25
CP of cap = 100x = Rs. 25
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