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X, Y and Z invested for certain time and the ratio of profit was 10 ∶ 15 ∶ 12. The amount Y invested was 15000 more than the amount invested by X, who invested 20,000 less than the amount invested by Z. X and Y invested for 5 and 3 years respectively. Find the time duration for which Z invested.

X, Y and Z invested for certain time and the ratio of profit was 10 ∶ 15 ∶ 12. The amount Y invested was 15000 more than the amount invested by X, who invested 20,000 less than the amount invested by Z. X and Y invested for 5 and 3 years respectively. Find the time duration for which Z invested. Correct Answer 2 years

Given:

The ratio of profit of X, Y, and Z = 10 ∶ 15 ∶ 12

Amount invested by Y = Amount invested by X + 15000

Amount invested by X = Amount invested by Z – 20000

X and Y invested for 5 and 3 years respectively.

Formula:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

Let the amount invested by X be x, and the time duration for which Z invested be t

ATQ,

Person

X

Y

Z

Amount

x

15000 + x

x + 20000

Time

5

3

t


Now,

Profit of X/Profit of Y = 10/15

⇒ 5x/45000 + 3x = 10/15

⇒ 3x = 30,000

⇒ X = 10,000

Profit share of X = 5 × 10,000 = 50,000

Profit share of Y = 25000 × 3 = 75000

Profit share of Z = 30,000t

Since we have the profit-sharing ratio 10 ∶ 15 ∶ 12

⇒ 50,000/30,000t = 10/12

⇒ t = 2

∴ Z invested for 2 years.

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