Question

A and B can do a piece of work in 12 days B and C in 15 days C and A in 20 days. A alone can do the work in?

Answer 1

Answer:

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Step-by-step explanation:

A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in :

[A]15\frac{2}{3} days

[B]5 days

[C]10 days

[D]7\frac{5}{6} days

10 days

According to question,

A and B can do a work in 12 days

∴ (A + B)’s one day’s work = \frac{1}{12}

Similarly, (B + C)’s one day’s work = \frac{1}{15}

and (C + A)’s one day’s work = \frac{1}{20}

On adding all three,

∴ 2 (A + B + C)’s one day’s work = \frac{1}{12}+ \frac{1}{15}+ \frac{1}{20}

= \frac{10+8+6}{120} = \frac{1}{5}

and (A + B + C)’s one day’s work = \frac{1}{10}

∴ A, B and C together can complete the work in 10 days.

Answer 2

30 days

Step by step instructions

Given:

A and B can do a work in 12 days ---(1)

B and C can do in 15 days ---(2)

C and A can do in 20 days ---(3)

To find:

In how many days A alone can do the work ?

Solution:

According to (1) , (2) and (3)

$\frac{1}{A} + \frac{1}{B} = \frac{1}{12} \: ---(1) \\ \\ \frac{1}{B} + \frac{1}{C} = \frac{1}{15} \: ---(2) \\ \\ \frac{1}{A} + \frac{1}{C} = \frac{1}{20} \: ---(3)$

Adding all equation,

$2( \frac{1}{A} + \frac{1}{B} + \frac{}{C} ) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} \\ \\ 2(\frac{1}{A} + \frac{1}{B} + \frac{1}{C} )= \frac{5 + 4 + 3}{60} \\ \\ 2(\frac{1}{A} + \frac{1}{B} + \frac{1}{C} ) = \frac{12}{60} \\ \\ [\text{Now, Putting the value of (2) }]\\ \\ \cancel{2}(\frac{1}{A} + \frac{1}{10} ) = \frac{\cancel{12}}{60} \\ \\ \frac{1}{} + \frac{1}{15} = \frac{ \cancel{6}}{\cancel{60}} \\ \\ \frac{?L1}{A} = \frac{1}{10} - \frac{1}{15} \\ \\ \frac{1}{A} = \frac{3 - 2}{30} \\ \\ \frac{1}{A} = \frac{1}{30} \\ \\ \therefore = 30$

Hence, A can complete the work in 30 days.