Question

Time and Work!

P and Q together can do a piece of work in 10 days,Q and R can do the same work together in 12 days,while P and R can do together in 15 days. How long each will take to do it seperately? ​

Answer 1

Solution :

We have,

$\sf \: (P + Q) \: can \: finish \: work \: in \: 10 \: days$

$\sf (Q + R ) \: can \: finish \: work \: in \: 12 \: days$

$\sf (P+ R ) \: can \: finish \: work \: in \: 15 \: days$

$\therefore \sf \: (P + Q)'s \: 1 \: day's \: work \: = \dfrac{1}{10}$

$\therefore \sf \: (Q + R)'s \: 1 \: day's \: work \: = \dfrac{1}{12}$

$\therefore \sf \: ( P \: + R)'s \: 1 \: day's \: work \: = \dfrac{1}{15}$

Adding,We get :

$\sf \: 2(P + Q + R)'s \: 1 \: day's \: work = \\ \hookrightarrow \: \sf \: \frac{1}{10} + \frac{1}{12} + \frac{1}{15}$

$\sf \hookrightarrow \: \dfrac{6 + 5 + 4}{60}$

$\sf \hookrightarrow \: \cancel \dfrac{15}{60} = \dfrac{1}{4}$

$\therefore \sf \: (P + Q + R)'s \: 1 \: day's \: work = \\ \sf \hookrightarrow \: \dfrac{1}{2 \times 4} = \dfrac{1}{8}$

Now,

P's 1 day's work = (P + Q + R)'s 1 day's work - (Q + R)'s 1 day's work

$\hookrightarrow \sf \: \dfrac{1}{8} - \dfrac{1}{12}$

$\hookrightarrow \sf \: \dfrac{3 - 2}{24} = \large \boxed{ \sf\dfrac{1}{24} }$

So,P alone can complete the work in 24 days.

Q's 1 day's work = (P + Q + R)'s 1 day's work - (P + R)'s 1 day's work

$\hookrightarrow \sf \: \dfrac{1}{8} - \dfrac{1}{15}$

$\hookrightarrow \sf \: \dfrac{15 - 8}{120} = \large \boxed{ \sf\dfrac{7}{120} }$

So,Q alone can complete the work in 120/7 days.

R's 1 day's work = (P + Q + R)'s 1 day's work - (P + Q)'s 1 day's work

$\hookrightarrow \sf \: \dfrac{1}{8} - \dfrac{1}{10}$

$\hookrightarrow \sf \: \dfrac{5 - 4}{40} = \large \boxed{ \sf\dfrac{1}{40} }$

So,R alone can complete the work in 40 days.

Answer 2

Answer:

Therefore, P alone can complete the work in 24 days.

Therefore, Q alone can complete the work in 120 / 7 days.

Therefore, R alone can complete the work in 40 days.

Step-by-step explanation:

According to the Question,

(P + Q) can finish the work in 10 days.

So, (P + Q) can finish the work in 1 day = 1/10

(Q + R) can finish the work in 12 days.

So, (Q + R) can finish the work in 1 day = 1/12

(P + R) can finish the work in 15 days.

So, (P + R) can finish the work in 1 day = 1/15

On adding, we get:

2 × (P + Q + R)'s one day's work = 1/10 + 1/12 + 1/15

=> 6 + 5 + 4 / 60

=> 15 / 60 = 1/4

(P + Q + R)'s one day's work = 1 / 2×4

(P + Q + R)'s one day's work = 1/8

Now,

P's one day's work

=> (P + Q + R)'s one day's work - (Q + R) can finish the work in 1 day

=> 1/8 - 1/12

=> 3 - 2 / 24

=> 1 / 24

Therefore, P alone can complete the work in 24 days.

Now,

Q's one day's work

=> (P + Q + R)'s one day's work - (P + R) can finish the work in 1 day

=> 1/8 - 1/15

=> 15 - 8 / 120

=> 7 / 120

Therefore, Q alone can complete the work in 120 / 7 days.

Now,

R's one day's work

=> (P + Q + R)'s one day's work - (P + Q) can finish the work in 1 day

=> 1/8 - 1/10

=> 5 - 4 / 40

=> 1 / 40

Therefore, R alone can complete the work in 40 days.