Arithmetic

Time & Work

Medium

Ram can do a piece of work in 10 days and Anshu in 20 days. They work together but 2 days before the completion of the work, Ram leaves and Anshu completes the work. In total how many days was the work completed?

6 days

4 days

8 days

3 days

✅ Correct Option: 3

Ram's work rate = $\dfrac{1}{10}$ of the work per day

Anshu's work rate = $\dfrac{1}{20}$ of the work per day

Combined rate when working together:

$\dfrac{1}{10} + \dfrac{1}{20}$

$= \dfrac{2}{20} + \dfrac{1}{20}$

$= \dfrac{3}{20}$ of the work per day

Let the total time taken = $x$ days

For $(x - 2)$ days: Both Ram and Anshu work together

For the last 2 days: Only Anshu works alone

Work done by both together = $(x - 2) \times \dfrac{3}{20}$

Work done by Anshu alone = $2 \times \dfrac{1}{20}$

$= \dfrac{2}{20}$

$= \dfrac{1}{10}$

Total work must equal 1:

$(x - 2) \times \dfrac{3}{20} + \dfrac{1}{10} = 1$

$(x - 2) \times \dfrac{3}{20} = 1 - \dfrac{1}{10}$

$(x - 2) \times \dfrac{3}{20} = \dfrac{9}{10}$

$x - 2 = \dfrac{9}{10} \times \dfrac{20}{3}$

$x - 2 = \dfrac{180}{30}$

$x - 2 = 6$

$x = 8$ days

Therefore, the work was completed in 8 days.

2023: 11 June Shift 2

A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days that A alone will take to finish the work is:

2026: 14 May Shift 2

A completes a work in 7 days. B completes the same work in 9 days. What will be the time taken in completing the same work if both A & B work together?

2025: 27 May Shift 1

P and Q together can do a piece of work in 60 days. Q and R together can do it in 120 days. P and R together can do it in 90 days. In what time can Q alone do the same work?

2023: 28 May Shift 1

Rakesh can do a certain job in 12 days. Vipin is 60% more efficient than Rakesh. How many days will Vipin alone take to do the same job ?

2025: 3 June Shift 1

X, Y and Z together can do a piece of work in 16 (4/11) days. X and Y together can do the same work in 20 days. In how many days will Z alone finish the 60% of the work?

2022: 8 Aug Shift 1

A and B can complete a piece of work in 30 days. B and C in 10 days, which C and A in 5 days. If all of them work together, the time taken in completing the work

Ram can do a piece of work in 10 days and Anshu in 20 days. They work together but 2 days before the completion of the work, Ram leaves and Anshu completes the work. In total how many days was the work completed?

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)