Question

AB and C invested their capital in ratio 2:3-4, at end of the business they received the profit
in the ratio 5:6:7. Find the ratio of time period for which they contributed their capitals.

Answer 1

Answer:

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let the capital of A = x

capital of B = y

and capital of C = z

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Given ratio of their capitals = 2 : 3 : 5

x : y : z = 2 : 3 : 5

let the P1 ,P2 ,P3 are the profits they received

at the end of the business terms.

Given, ratio of their profits = 5 : 3 : 12

P1 : P2 : P3 = 5 : 3 : 12

According to the formula ,

Required ratio will be

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= P1 / x : P2 / y : P3 / z

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= 5 / 2 : 3 / 3 : 12 / 5

= 5 / 2 : 1 : 12 / 5

= 5 × 5 : 2 × 5 : 2 × 12

= 25 : 10 : 24

therefore,

ratio of time for which they contributed

= 25 : 10 : 24

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Your Answer : (d) 25 : 10 : 24

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Answer 2

Given,

The ratio of their capitals = $2 : 3 : 4$

Let,

capital of $A$ = $x$

capital of $B$ = $y$ , and      

capital of $C$ = $z$

$x : y : z$ = $2 : 3 : 4$

Also Given,

The ratio of their profits = $5 : 6 : 7$

Let the $P1, P2$ and $P3$ are the profits they received at the end of the business terms.

$P1 : P2 : P3$ = $5 : 6 : 7$

According to the formula,

The required ratio will be = $\frac{P1}{x} : \frac{P2}{y} : \frac{P3}{z}$

= $\frac{5}{2} : \frac{6}{3} : \frac{4}{7}$

= $\frac{5}{2} : 2 : \frac{4}{7}$

= $\frac{5}{2}$×$2$ : $2$×$2$ : $\frac{4}{7}$×$2$

= $5 : 4 : \frac{8}{7}$

= $35 : 28 : 8$

Hence, the ratio of time for which they contributed = $35 : 28 : 8$

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