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Option 3 : Quantity A = Quantity B or No relation
Quantity A:
Let the Krishna invested his capital for the x months.
Ratio of the investment of Gopal and Krishna = 40 × 15 : 60 × x = 10 : x
Ratio of the profit of Gopal and Krishna = (100 - 400/9 : 400/9) = 500/9 : 400/9 = 5 : 4
Ratio of the investment is equal to the ratio of profit so,
⇒ 10/x = 5 : 4
⇒ x = 8
Krishna invested his capital for the 8 months.
Quantity B:
Let the number be x then,
⇒ (x + 50/100x) × 100 = 1200
⇒ x = 8
∴ Quantity A = Quantity B
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