Question

A can do a piece of work in 4 hours; B and C together can do it in 3 hours,
while A and C together can do it 2 hours. How long will B alone take to do it?
(b) 10 hours (c) 12 hours (d) 24 hours
​

Answer 1

Given:

✰ A can do a piece of work in 4 hours.

✰ B and C together can do it in 3 hours.

✰ A and C together can do it 2 hours.

To find:

✠ How long will B alone take to do a piece of work.

How to solve?

• A can do a piece of work in 4 hours so first we will find A's one hour's work.

• As B and C together can do it in 3 hours, so then we will find (B + C)'s is one hour's work.

• A and C together can do it 2 hours, so after that (A + C)'s one hour work.

• Subtract A's one hour work from (A + C)'s. Here A's work will get substracted, then we will be left with C's one of work.

• At last to find B's one hour work, we will substract C's one hour work from (B + C)'s one hour work, then C's will get substract and we are finally left with B's one hour work.

Solution:

❖ One day is work = 1/number of days required to complete the work

A can do a piece of work in 4 hours.

• A's one hour work = 1/4

B and C together can do it in 3 hours.

• (B + C)'s one hour work = 1/3

A and C together can do it 2 hours.

• (A + C)'s one hour work = 1/2

∴ C's one hour work = (A + C)'s one hour work - A can do a piece of work in 4 hours

• C's one hour work = 1/2 - 1/4
• C's one hour work = (2-1)/4
• C's one hour work = 1/4

Now,

B's one hour work = (B + C)'s one hour work - C's one hour work

• B's one hour work = 1/3 - 1/4
• B's one hour work = (4-3)/12
• B's one hour work = 1/12

If one's day work = 1/12

then, the work can be completed in 12 days

So,

∴ B alone can do the piece of work in 12 days

Option (c) is correct ✓

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Answer 2

Given Question :-

• A can do a piece of work in four hours. B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will it take B alone to do it?

Answer :-

Given :-

• A can do a piece of work in four hours.
• B and C together can do it in 3 hours.
• A and C together can do it in 2 hours.

To find :-

• How long will it take B alone to do it?

Solution :-

Let a,b & c be the number of hours taken by A, B & C alone to complete the work alone.

Given, A can do a piece of work in four hours.

$:  \implies \boxed{ \red{\bf \: \dfrac{1}{a} = \dfrac{1}{4}}} - - (i)$

Now,

B and C together can do it in 3 hours,

$:  \implies \boxed{ \red{ \bf \: \dfrac{1}{b} + \dfrac{1}{c} = \dfrac{1}{3} }} - - (ii)$

Also,

A and C together can do it in 2 hours,

$:  \implies \boxed{ \red{ \bf \: \dfrac{1}{a} + \dfrac{1}{c} = \dfrac{1}{2} }}$

$:  \implies \tt \: \dfrac{1}{4} + \dfrac{1}{c} = \dfrac{1}{2} \: \: \: \: \: \{using \: (i) \}$

$:  \implies \tt \: \dfrac{1}{c} = \dfrac{1}{2} - \dfrac{1}{4} \: \: \: \: \:$

$:  \implies \tt \: \dfrac{1}{c} = \dfrac{2 - 1}{4}$

$:  \implies \boxed{ \red{ \bf \: \dfrac{1}{c} = \dfrac{1}{4} }} - - (iii)$

Substituting this value in equation (ii), we get

$:  \implies { { \bf \: \dfrac{1}{b} + \dfrac{1}{4} = \dfrac{1}{3} }}$

$:  \implies { { \bf \: \dfrac{1}{b} = \dfrac{1}{3} - \dfrac{1}{4} }}$

$:  \implies { { \bf \: \dfrac{1}{b} = \dfrac{4 - 3}{12} }}$

$:  \implies \boxed{ \purple{ { { \bf \: \dfrac{1}{b} = \dfrac{1}{12} }} }}$

● Hence, The number of days taken by B to complete the work alone is 12 hours.