Learn the Time and Work concept easily by solving various problems. The basic equation of the time and work problems are

(i) If the one man can do the work in ‘x’ days, then the work completed in one day by one man is equal to \(\frac{1}{x}\).

(ii) Work done by one person is ‘x’ units, then the time taken by the person is equal to \(\frac{1}{x}\).

The Time and Work concept is a little bit difficult concept. But if you clearly understand the basic relation between time and work, then you can easily solve the questions.

Must Read:

- Calculate Time to Complete a Work
- Calculate Work Done in a Given Time
- Problems on Time required to Complete a Piece a Work

## Time and Work Questions and Answers

In this section, we are providing the different types of questions related to time and work with the solutions. Follow the below examples and solve the Time and Work problems very quickly. Let us see the questions.

**Example 1.**

A works three times better than B. By working A and B together, they can finish the piece of work in 18 days. Find the time to finish the work by A and B alone?

**Solution:**

Let us consider the B work as a = ‘x’.

A work as b = ‘3x’.

So, B’s one day work = \(\frac{ 1 }{ a }\) = \(\frac{ 1 }{ x }\).

A’s one day work = \(\frac{ 1 }{ b }\) = \(\frac{ 1 }{ 3x }\).

By working together, A and B can complete the work in 18 days.

So, A and B can complete the work in one day = \(\frac{ 1 }{ 18 }\).

Work done by A and B in one day = \(\frac{ 1 }{ a }\) + \(\frac{ 1 }{ b }\) = \(\frac{ 1 }{ 18 }\).

The ration between A and B’s one day work = 3 : 1

A can complete work in one day is equal to \(\frac{ 3 }{ 4 }\) × \(\frac{ 1 }{ 18 }\).

= \(\frac{ 1 }{ 24 }\).

Therefore, A alone can complete the total work in 24 days.

So, A can complete the work in one day is equal to the \(\frac{ 1 }{ 24 }\)th part of the work.

B can complete work in one day is equal to \(\frac{ 1 }{ 4 }\) × \(\frac{ 1 }{ 18 }\) .

= \(\frac{ 1 }{ 72 }\).

So, A can complete the work in one day is equal to the \(\frac{ 1 }{ 72 }\)nd part of the work.

Therefore, B alone can complete the total work in 72 days.

**Example 2.**

Andrew, Brew, Catherin can build a wall in 20 days, 25 days, and 30 days respectively. If all three work together, then they can get the $1200 for complete work. Find the individual payment and number of working days to complete the work together?

**Solution:**

As per the given information, Andrew can take the time to complete the work in 20 days.

Work done by Andrew in one day = \(\frac{ 1 }{ 20 }\).

The brew can take time to complete the work in 25 days.

Brew can complete the work in one day = \(\frac{ 1 }{ 25 }\).

Catherin can take time to complete the work in 30 days.

Catherin can finish the work in one day = \(\frac{ 1 }{ 30 }\).

Ratio of one day work by Andrew, Brew, and Catherin = \(\frac{ 1 }{ 20 }\) : \(\frac{ 1 }{ 25 }\) :\(\frac{ 1 }{ 30 }\).

= 15 : 12 : 10.

Sum of the ratio = 15 + 12 + 10 = 37.

Amount to be taken by the three members for the total work = $1200.

Andrew’s Payment = \(\frac{ 15 }{ 37 }\)× 1200 = $486.

Brew’s Payment = \(\frac{ 12 }{ 37 }\) × 1200 = $389.

Catherin’s Payment = \(\frac{ 10 }{ 37 }\) × 1200 = $324.

Therefore, the Individual payment of Andrew, Brew, and Catherin is $486, $389, and $324.

Three members are working together. That is

(Andrew + Brew + Catherin)’s work for one day = \(\frac{ 1 }{ 20 }\) + \(\frac{ 1 }{ 25 }\) + \(\frac{ 1 }{ 30 }\).

= \(\frac{ 15 + 12 + 10 }{ 300 }\).

= \(\frac{ 37 }{ 300 }\).

So, Andrew, Brew, Catherin can complete the work in one day = \(\frac{ 37 }{ 300 }\).

Therefore, Andrew, Brew, and Catherin can complete the total work in \(\frac{ 300 }{ 37 }\) days = 8 days.

**Example 3.**

John can finish the work in 4 days by working 8 hours per day. Liam can complete the same work in 6 days by working the 10 hours per day. Calculate the time to complete the work by John and Liam together?

**Solution:**

As per the information, John can complete the work in 4 days by working 8 hours per day = (4 × 8) = 32 hours.

Liam can complete the work in 6 days by working 10 hours per day = (6 × 10) = 60 hours.

Work done by John in one hour = \(\frac{ 1 }{ 32 }\).

Work done by Liam in one hour = \(\frac{ 1 }{ 60 }\).

John and Liam both can complete the work in one hour = \(\frac{ 1 }{ 32 }\) + \(\frac{ 1 }{ 60 }\).

= \(\frac{ 15 + 8 }{ 480 }\).

= \(\frac{ 23 }{ 480 }\).

= 21 hours.

John and Liam together can complete the work 21 hours.

**Example 4.**

15 men are taken 10 days of time to complete the work and the same work is completed by 10 women in 15 days. 5 men and 5 women are worked for 6 days. Calculate how many men are required to complete the remaining work in one day?

**Solution:**

As per the information, 15 men can complete the work in 10 days. That is 15 × 10 = 150.

So, 1 men one day’s work = \(\frac{ 1 }{ 150 }\).

10 women can complete the same work in 15 days. That us 10 × 15 = 150.

So, 1 women can complete the work in one day = \(\frac{ 1 }{ 150 }\).

5 men and 5 women are working together for 5 days = 5(\(\frac{ 1 }{ 150 }\) + \(\frac{ 1 }{ 150 }\)).

= 5 \(\frac{ 2 }{ 150 }\).

= \(\frac{ 1 }{ 15 }\).

Remaining work = 1- \(\frac{ 1 }{ 15 }\) = \(\frac{ 14 }{ 15 }\).

5 men and 5 women can complete the work in one day = 1 (\(\frac{ 1 }{ 150 }\) + \(\frac{ 1 }{ 150 }\)).

= \(\frac{ 2 }{ 150 }\).

= \(\frac{ 1 }{ 75 }\).

So, the remaining work for one day = \(\frac{ 14 }{ 15 }\) – \(\frac{ 1 }{ 75 }\).

= \(\frac{ 70 – 1 }{ 75 }\).

= \(\frac{ 69 }{ 75 }\).

1 man can do the work in one day is equal to \(\frac{ 1 }{ 150 }\).

So, 150 ×\(\frac{ 69 }{ 75 }\) = 2 × 69 = 138 men.

Therefore, 138 men are required to complete the remaining work in one day.

**Example 5.**

(x + 2) women can complete the work in x days. (x – 7) women can complete 50% of the same work in (x + 10) days. In how many days, (x + 5) women can complete the work?

**Solution:**

As per the given information, (x + 2) women can finish the work in ‘x’ days. That is = (x + 2) x.

(x – 7) women can finish the 75% of the same work in (x +10) days. That is

\(\frac{ 3 }{ 4 }\) × (x + 2) x = (x – 7) (x + 10).

\(\frac{ 3 }{ 4 }\) × x^2 + 2x = x^2 + 10x – 7x – 70.

3(x^2 + 2x) = 4(x^2 +3x -70).

3x^2 + 6x = 4x^2 + 12x – 280.

4x^2 – 3x^2 +12x – 6x -280 = 0.

X^2 +6x – 280 = 0.

X^2 + 20x – 14x – 280= 0.

x(x + 20) -14(x + 20) = 0.

X = -20 or 14.

Total work is equal to (x + 2)x = (14 + 2) (14) = (16)(14) = 224 units.

So, (x + 5) = 14 + 5 = 19 women

\(\frac{ 224 }{ 19 }\) = 11.7 days.

Therefore, 19 women can finish the work in 11.7 days.