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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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