Arithmetic

Time & Work

Medium

P completed $\frac{2}{5}$ part of certain work in 12 days. Further, Q completed the rest of the work in 18 days. In how many days could P and Q complete the work, if they worked together?

✅ Correct Option: 4

P completed $\frac{2}{5}$ of the work in 12 days.

Q completed the remaining part.

Remaining work $= 1 - \frac{2}{5} = \frac{3}{5}$

Q completed $\frac{3}{5}$ of the work in 18 days.

P's work rate per day:

$= \frac{2/5}{12}$

$= \frac{2}{5} \times \frac{1}{12}$

$= \frac{2}{60}$

$= \frac{1}{30}$ of the work per day

P alone can complete the entire work in 30 days.

Q's work rate per day:

$= \frac{3/5}{18}$

$= \frac{3}{5} \times \frac{1}{18}$

$= \frac{3}{90}$

$= \frac{1}{30}$ of the work per day

Q alone can complete the entire work in 30 days.

Combined work rate when P and Q work together:

$= \frac{1}{30} + \frac{1}{30}$

$= \frac{2}{30}$

$= \frac{1}{15}$ of the work per day

Days needed to complete the work together:

$= \frac{1}{\frac{1}{15}}$

$= 1 \times 15$

$= 15$ days

Therefore, P and Q working together can complete the work in 15 days.

2026: 25 May Shift 2

A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same work ?

2023: 15 June Shift 2

A completes $\frac{7}{20}$ of a work in 10 days. Then he completes the remaining work with the help of B in 5 days. The time required for A and B together to complete the entire work is:

2025: 20 May Shift 2

Ram, Shyam and Hari can complete a work in 20, 25 and 30 days, respectively.

Consider the following statements:

(A) Ram and Shyam together will complete the work in $11\frac{1}{9}$ days.

(B) Shyam and Hari together will complete the work in 14 days.

Choose the correct answer from the options given below:

2022: 26 Aug Shift 1

A can finish a work in 16 days and B can do same work in half the time taken by A. Then, working together, what part of same work they can finish in a day ?

2025: 15 May Shift 1

P and Q together can do a job in 6 days. Q and R can finish the same job in 60/7 days. P started the work and worked for 3 days. Q and R continued for 6 days and finish the work. Then, the difference of days in which R and P , independently can complete the job is:

2025: 26 May Shift 1

A can complete a work in 16 days, working 6 hours a day. B can complete the same work in 12 days, working 9 hours a day. If both A and B work together, working 8 hours a day, in how many days can they complete the work?

P completed 25\frac{2}{5}52​ part of certain work in 12 days. Further, Q completed the rest of the work in 18 days. In how many days could P and Q complete the work, if they worked together?

Solution

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Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)

P completed $\frac{2}{5}$ part of certain work in 12 days. Further, Q completed the rest of the work in 18 days. In how many days could P and Q complete the work, if they worked together?