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Bunuel
The rate of P is twice that of Q and the rate of Q is thrice that of R. If P, Q and R together can complete the work in 30 days, then in how many days P alone can do the work?

A. 52 days
B. 50 days
C. 45 days
D. 42 days
E. 30 days


Are You Up For the Challenge: 700 Level Questions

\(\frac{1}{P}=2(\frac{1}{Q})\)

\(\frac{1}{Q}= 3(\frac{1}{R})\)

--> \(Q= 2P\)
--> \(R = 3Q = 6P\)
---------------------------
\(\frac{1}{P}+\frac{1}{Q}+\frac{1}{R}= \frac{1}{30}\)

--> \(\frac{1}{P}+ \frac{1}{2P}+ \frac{1}{ 6P}= \frac{1}{30}\)

\(\frac{(6+3+1)}{6P}= \frac{1}{30}\)
--> \(P = 50\)

Answer (B)
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Bunuel
The rate of P is twice that of Q and the rate of Q is thrice that of R. If P, Q and R together can complete the work in 30 days, then in how many days P alone can do the work?

A. 52 days
B. 50 days
C. 45 days
D. 42 days
E. 30 days


Are You Up For the Challenge: 700 Level Questions

given rate of P = 2 Rate of q
rate of Q = 3 rate of R
let rate of R = x
so rate of Q = 3x and rate of P = 6x
together rate ; 6x+3x+x ; 10 x ( 10 work per day)
work completed in 30 days ;
which means the total work was ; 30*10 ; 300 units
so rate of P must be 300/6 ; 50
OPTION B
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Bunuel
The rate of P is twice that of Q and the rate of Q is thrice that of R. If P, Q and R together can complete the work in 30 days, then in how many days P alone can do the work?

A. 52 days
B. 50 days
C. 45 days
D. 42 days
E. 30 days


If we let R = the number of days in which R can complete the work by himself, then 1/R = the rate of R, 3/R = the rate of Q and 2(3/R) = 6/R = the rate of P, and we can create the equation:

6/R + 3/R + 1/R = 1/30

10/R = 1/30

300 = R

Thus, the rate of P is 6/300 = 1/50, so P can do the job in 50 days.

Answer: B
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