Question

3) 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?​

Answer 1

Answer:

R will get 500

Step-by-step explanation:

Given,

P alone can finish a job in 12 days

P=1/12

Q can do so in  16 days.

Q=1/16

With the help of R, they have finished the job in  4 days

P+Q+R=1/4

1/12+1/16+R=1/4

R=1/4-1/12-1/16

R=5/48

a contract price of 1,200

ratio between P,Q,R is

1/12:1/16:5/48

LCM=48

1/12*48:1/16*48:5/48*48

4:3:5

Let 4p:3p:5p are amounts of P,Q,R

total 4p+3p+5p=1200

         12p=1200

          p=100

R=5p

  =5*100

  =500

Answer 2

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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