Arithmetic

Time & Work

Medium

A and B can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, find the number of days in which B alone can do the work?

10 days

20 days

5 days

12 days

✅ Correct Option: 2

Think of work as a pizza (total = 1 whole pizza). Each person completes a certain portion per day.

Given information:

A and B together finish in 12 days
B and C together finish in 15 days
A is twice as fast as C

Let C's work rate = $c$ (portion of work/day)

Let A's work rate = $2c$ (since A is twice as good as C)

Let B's work rate = $b$ (portion of work/day)

From "A and B complete in 12 days":

$(2c + b) \times 12 = 1$

$2c + b = \dfrac{1}{12}$ ... Equation (1)

From "B and C complete in 15 days":

$(b + c) \times 15 = 1$

$b + c = \dfrac{1}{15}$ ... Equation (2)

Subtract Equation (2) from Equation (1):

$(2c + b) - (c + b) = \dfrac{1}{12} - \dfrac{1}{15}$

$c = \dfrac{1}{12} - \dfrac{1}{15}$

$c = \dfrac{5}{60} - \dfrac{4}{60}$

$c = \dfrac{1}{60}$

Substitute $c = \dfrac{1}{60}$ into Equation (2):

$b + \dfrac{1}{60} = \dfrac{1}{15}$

$b = \dfrac{1}{15} - \dfrac{1}{60}$

$b = \dfrac{4}{60} - \dfrac{1}{60}$

$b = \dfrac{3}{60}$

$b = \dfrac{1}{20}$

If B's rate = $\dfrac{1}{20}$ work per day, then B completes 1 full work in 20 days.

Therefore, B alone can do the work in 20 days.

2025: 13 May Shift 2

'A' can build up a structure in 8 days and 'B' can break it in 3 days. 'A' worked building for 4 days and then 'B' joined and start breaking while 'A' kept building for another 2 days. In how many days will 'A' alone build up the remaining part of the structure?

2022: 20 Aug Shift 1

Find in whichever condition/conditions filling of water tank is/are possible :

A. One tap filling the tank in 2 liter / minute.

B. One tap filling the tank in 15 liter / minute and one tap emptying the tank with speed 1 liter / minute.

C. Two tap filling the tank with uniform speed of 4litre/minute and one tap emptying the tank with speed of 500 ml / sec.

D. One tap filling the tank in 2 liter / minute and one tap emptying the tank with speed 4 liter / minute.

Choose the correct answer from the options given below:

2025: 29 May Shift 1

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?

2026: 31 May Shift 2

A is twice as good as a workman B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?

2026: 12 May Shift 2

X, Y and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days can Z alone finish the same work?

2026: 21 May Shift 2

A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C worked together for 2 days and then A was replaced by B. In how many days, altogether, was the work completed?

A and B can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, find the number of days in which B alone can do the work?

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)