Question

2. A, B and C can do a piece of work in 12 days, 15 days and 10 days respectively. In what time will
they all together finish it?​

Answer 1

Answer:

$\huge{\pink{\green{\sf{\therefore Time\:taken=4\:days}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In the given question information given about 3 people and their completion of time to do the work is given.

• So, we have to find the time taken to do the same work if they work together.

$\underline \bold{Given : } \\ \implies A\: can \: do \: a \: work \: = 12 \: days \\ \implies B\: can \: do \: same \: work = 15 \: days \\ \implies C \:do \: the \: same \: work = 10 \: days \\ \\ \underline \bold{To \: Find : } \\ \implies Time \: taken \: if \: they \: work \: together = ?$

• According to given question :

$\bold{For \: A} \\ \implies Work \: do \: in \: one \: day = \frac{1}{12} - - - - (1) \\ \\ \bold{For \: B}\\ \implies Work \: do \: in \: one \: day = \frac{1}{15} - - - - (2) \\ \\ \bold{ For \: C} \\ \implies Work \:do \: in \: one \: day = \frac{1}{10} - - - - (3) \\ \\ \bold{ If \: they \: work \: together } \\ \bold {Adding \: (1)(2) \: and \: (3)} \\ \implies \frac{1}{12} + \frac{1}{15} + \frac{1}{10} \\ \bold {Take \: Lcm \: of \: 12,15\: and \: 10 = 60}\\ \implies \frac{5 + 4 + 6}{60} \\ \implies \frac{15}{60} \\ \implies \frac{60}{15} \\ \bold{\implies 4 \: days} \\ \\ \bold{\therefore In \: 4 \:days \: they \: complete \: the \: work}$

Answer 2

A fo a piece of work in 12 days.

So,

Work done by A in 1 day = $\dfrac{1}{12}$ days ____ (eq 1)

Similarly,

B do a piece of work in 15 days.

Work done by B in 1 day = $\dfrac{1}{15}$ days ____ (eq 2)

C do a piece of work in 10 days.

Work done by C in 1 day = $\dfrac{1}{10}$ days _____ (eq 3)

We have to find that in how many days A, B and C all together to finish the work.

We have to simply add (eq 1), (eq 2) and (eq 3)

=> $\dfrac{1}{12}\:+\:\dfrac{1}{15}\:+\:\dfrac{1}{10}$

=> $\dfrac{5\:+\:4\:+\:6}{60}$

=> $\dfrac{15}{60}$

=> $\dfrac{1}{4}$

=> 4 days

∴ In 4 days A, B and C will finish the work all together.