Question

P can complete a job in 27 days . He starts it and after three days Q joins him . They work together for six days . P then leaves and R takes his place . Q and R complete the job in 12 more days

If q takes at most 54 days to complete the job.what cannot be the possible value of number of days taken by r to complete the job? a:36 b:34 c:40 d:38​

Answer 1

Solution :-

given that,

→ P completes the job in = 27 days .

so,

→ Per day work of P = (1/27) units

similarly,

→ Q takes to complete the job = 54 days.

so,

→ Per day work of Q = (1/54) units.

then,

→ 3P + 6(P + Q) + 12(Q + R) = 1

putting values ,

→ 3*(1/27) + 6[(1/27) + (1/54)] + 12[(1/54) + R] = 1

→ (1/9) + 6 * (3/54) + (12/54) + (12/R) = 1

→ (1/9) + (1/3) + (2/9) + (12/R) = 1

→ (1 + 3 + 2)/9 + (12/R) = 1

→ (6/9) + (12/R) = 1

→ (12/R) = 1 - (2/3)

→ (12/R) = (1/3)

→ R = 36 days.

therefore, If we take q days less than or more than 54 , 36 days can not be the value of days taken by r .

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