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In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: P and Q invested money in a business, such that P invested Rs. 10000 more than Q. After 6 months, if they received their profits in the ratio 5 ∶ 3, how much money did P invested? Quantity B: X and Y invested money in a business in the ratio 5 ∶ 6. If after 2 years, X received a profit of Rs. 20000, how much profit did Y received?

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: P and Q invested money in a business, such that P invested Rs. 10000 more than Q. After 6 months, if they received their profits in the ratio 5 ∶ 3, how much money did P invested? Quantity B: X and Y invested money in a business in the ratio 5 ∶ 6. If after 2 years, X received a profit of Rs. 20000, how much profit did Y received? Correct Answer Quantity A > Quantity B

Solving for Quantity A:

Let P’s initial investment be Rs. ‘x’

⇒ Q’s initial investment = Rs. (10000 – x)

Now,

P’s total capital investment = 6x

Q’s total capital investment = 6(x – 10000)

But,

Ratio of profits = Ratio of total capital investments

⇒ 5/3 = 6x/6(x – 10000)

⇒ 5(x – 10000) = 3x

⇒ 5x – 50000 = 3x

⇒ 2x = 50000

⇒ x = 50000/2 = Rs. 25000

⇒ Quantity A = Rs. 25000

Solving for Quantity B:

Let the initial investment of P and Q be Rs. ‘5x’ and Rs. ‘6x’ respectively

P’s total capital investment = 24 × 5x = 120x

Q’s total capital investment = 24 × 6x = 144x

But, Ratio of profits = Ratio of total capital investments

⇒ 20000/Y’s profit = 120x/144x

⇒ Y’s profit = 20000 × 6/5 = Rs. 24000

⇒ Quantity B = Rs. 24000

∴ Quantity A > Quantity B

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