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A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the…

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A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task along to the number of days taken by B when completing the same task alone?
  • A2 : 5
  • B2 : 7
  • C3 : 7
  • D1 : 5
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Discussion 2

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CCommunity
Solution
Let the work completed by A in one day = $\frac{1}{A}$

Let the work completed by B in one day = $\frac{1}{B}$

Let the work completed by C in one day = $\frac{1}{C}$

$\frac{1}{A}$ + $\frac{1}{B}$ = $\frac{1}{20}$

$\frac{1}{B}$ + $\frac{1}{C}$ = $\frac{1}{30}$

$\frac{1}{A}$ + $\frac{1}{C}$ = $\frac{1}{40}$

Solving the above equations we get $\frac{1}{A}$ = $\frac{1}{24}$

A = 24

Similarly B = 120 and C = 60
0
CCommunity
Solution
Let the work completed by A in one day = $\frac{1}{A}$

Let the work completed by B in one day = $\frac{1}{B}$

Let the work completed by C in one day = $\frac{1}{C}$

$\frac{1}{A}$ + $\frac{1}{B}$ = $\frac{1}{20}$

$\frac{1}{B}$ + $\frac{1}{C}$ = $\frac{1}{30}$

$\frac{1}{A}$ + $\frac{1}{C}$ = $\frac{1}{40}$

Solving the above equations we get $\frac{1}{A}$ = $\frac{1}{24}$

A = 24

Similarly B = 120 and C = 60