The rate of P is twice that of Q and the rate of Q is thrice that of R

Question

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

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yashikaaggarwal · Answer

Let the Work done by C is x
Therefore B will be 3x.
And A will be 6x.
Their Ratio is 6:3:1
They do 6+3+1=10 work a day
Work is completed in 30 days.
So they did 30*10=300 work during the Given period.
A could have done work in 300/6=50 days

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MrSengupta · Answer

The answer is (B) .

Let the time taken by R is r units/day . Therefore Q=3r and P=6r.

Therefore total work = 30r+90r+180r=300r

Therefore P takes: 300r/6r =50 days

lacktutor · Answer

\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)

Archit3110 · Answer

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

ScottTargetTestPrep · Answer

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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The rate of P is twice that of Q and the rate of Q is thrice that of R

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