Question

A and B can do a work in 10 days,
B and C can do it in 12 days, C
and A can do it in 15 days. IfA, B
and C work together, they will
complete the work in:
(a) 15 days (b) 8 days
(c) 10 days (d) 12 days​

Answer 1

Answer:

8 days

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Answer 2

Question :

A and B can do a Work in 10 days, B and C can do it in 12 days, C and A can do it in 15 days.

If A, B, and C work together, they will complete the Work in -

(a) 15 days

(b) 8 days

(c) 10 days

(d) 12 days

$\begin{gathered} \end{gathered}$

Solution :

Time taken by (A and B) to finish the Work = 10 days

Time taken by (B and C) to finish the Work = 12 days

Time taken by (C and A) to finish the Work = 15 days

$\begin{gathered} \end{gathered}$

∴ (A and B)'s 1 day's Work = $\bf \dfrac{1}{10}$

(B and C)'s 1 day's Work = $\bf \dfrac{1}{12}$

(C and A)'s 1 day's Work = $\bf \dfrac{1}{15}$

$\begin{gathered} \end{gathered}$

Adding these, we get -

$\begin{aligned} \text{2(A + B + C)'s 1 day's Work} &= \Big (\dfrac{1}{10} + \dfrac{1}{12} + \dfrac{1}{15} \Big )\\\\&\Rightarrow \dfrac{6+5+4}{60} \\ &\boxed {\text{LCM of 10, 12, and 15 = 60}}\\\\&\Rightarrow \dfrac{15}{60} = \bf \dfrac{1}{4} \end{aligned}$

$\begin{gathered} \end{gathered}$

$\begin{aligned} \text{(A + B + C)'s 1 day's Work} &= \Big (\dfrac{1}{2} \times \dfrac{1}{4} \Big )\\\\&= \bf \dfrac{1}{8} \end{aligned}$

$\Longrightarrow$ A, B, and C together can finish the Work in 8 days.

∴ Option B is the Right Answer. . .

$\begin{gathered} \end{gathered}$

Additional Information :

Some General Rules on Time and Work :-

(i) Suppose A can finish a Work in n days.

Then, Work done by A in 1 day = $\dfrac{1}{n}$

$\begin{gathered} \end{gathered}$

(ii) Suppose the Work done by A in 1 day is $\dfrac{1}{n}$.

Then, Time taken by A to finish the Whole Work = n days.