Question

1) P alone can finish a job in 12 days while Q can do so in
16 days. With the help of R, they have finished the job in
4 days for a contract price of 1,200. How much should
R get out of it?
A) 300
B 400
C) 500
D) 600​

Answer 1

Given :-

• P alone can finish job in = 12 days.
• Q alone can finish in = 16 days.
• With the help of R, they have finished the job in 4 days for a contract price of 1,200.

To Find :-

• How much should R get out of it ?

Solution :-

LCM of 12 and 16 = 48 units = Let total work

so,

→ Efficiency of P = (Total work)/(Total days) = 48/12 = 4 units/day.

and,

→ Efficiency of Q = (Total work)/(Total days) = 48/16 = 3 units/day.

Now, Let us assume that , Efficiency of R is x units/day.

then,

→ 4(4 + 3 + x) = 48 units

→ 4 + 3 + x = 12

→ x = 12 - 7

→ x = 5 units/day .

Therefore, we can conclude that, they will get amount in the ratio of their efficiency .

hence,

→ Share of R = (5/12) * 1200 = Rs.500 (C) (Ans.)

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Answer 2

Given :  P alone can finish a job in 12 days while Q can do so in 16 days.

With the help of R, they have finished the job in 4 days for a contract price of 1,200

To Find : How much should R get out of it?

A) 300

B) 400

C) 500

D) 600​

Solution:

P alone can finish a job in 12 days

=> P  1  Day work  =  1/12

Q alone can finish a job in 16 days

=>Q  1  Day work  =  1/16

R alone can finish a job in R days

=>R  1  Day work  =  1/R

1/12  + 1/16 + 1/R  = 1/4

=> 1/R = 1/4  - 1/12  - 1/16

=> 1/R =  ( 12 - 4 - 3)/48

=> 1/R  = 5/48

=>

Work of each in 4 Days

P work  = 4/12   = 16/48

Q work = 4/16  =   12/48

R work  = 4(5/48) =   20/48

P : Q :  R = 16 : 12 : 20

R share = (20/48) * 1200

= 500

R should get = Rs 500

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