Time & Work, Ex-13B

Question

1. A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in?

2. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

3. A alone can finish a piece of work in 10 days which B alone can do in 15 days. If they work together and finish it, then out of total wages of ₹3000, A will get:

4. 3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it?

5. A can do a piece of work in 15 days. B is 50% more efficient than A. B can finish it in:

Answer 1

1. Number of days A requires to do piece of work = 16 days

Number of days B requires to do piece of work = 12 days

Let us consider number of days C requires to do piece of work = x days

Number of days A,B and C together requires to do the piece of work = 6 days

∴ We can calculate, work done by A in 1 day = \(\frac{1}{16}\)

Work done by B in 1 day = \(\frac{1}{12}\)

Work done by C in 1 day = \(\frac{1}{x}\)

Work done by A,B and C together in a 1 day = \(\frac{1}{6}\)

Now, work done by A,B and C together in 1 day is also equal to the sum of work done by each of them in 1 day = \(\frac{1}{6}\) + \(\frac{1}{12}\) + \(\frac{1}{x}\) = \(\frac{7}{48}\) + \(\frac{1}{x}\)

Therefore,

7/48 + 1/x = 1/6

(7x + 48)/48x = 1/6

42x + 288 = 48x

6x = 288

x = 288/6 = 48

∴C can do the work in 48 days.

2. Given:

Time taken to complete a piece of work by B = x 

Time taken to complete same work  by A = x + 50%

Let us consider the number of days B requires to complete the work = x days 

So, number of days A requires to complete the work = x + (50/100)x = 1.5x

We can calculate, work done by A in 1 day = 1/1.5x = 2/3x

And work done by B in 1 day = 1/x

We know that the number of days A and B together requires to do work = 18 days 

So, work done by both A and B in 1 day = 1/18

⇒ 2/3x + 1/x = 1/18

⇒ 5/3x = 1/18

⇒ x = (5× 18)/3

⇒ x = 30

∴ B requires 30 days to complete the work.

(3) A's 1 day's work = 1/10

B's 1 day's work = 1/15

Ratio of wages of A and B = 1/10 : 1/15 = 3 : 2

A's share = Rs.(3000 × 3/5) = Rs.1800

(4) 3 men ≡ 5 women

1 man = 5/3 × 6 = 10 women

(6 men + 5 women) ≡ 15 women

5 women can do the work in 12 days.

1 woman can do it in 12 × 5 days.

Therefore, 15 women can do it in 12×5/15 = 4 days

(5) 

Given, A can do a certain work in 15 days.

In one day, A can complete part of work = 1/15

Given, B is 50% more efficient than A.

∴ Part of work completed by B in one day = 1.5 × A’s one day work

Part of work completed by B in one day = 1.5 × (1/15) = 1/10

Thus , working together in 1 day they complete part of work = (1/15) + (1/10) = 5/30

Working together in 1 day they complete part of work = 1/6

∴ They will finish the work in 6 days working together.