Exercise : 3


1. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A along could have done in 23 days?
(a) 11 days
(b) 13 days
(c) 20317 days
(d) 12 days
(e) None of these
Ans.b

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.

Then, 10 : 13 : : 23 : x ⇒ x = \(\frac{\left(23 \times 13 \right)}{10}\) ⇒ x = 29910

A’s 1 day’s work = 123; B’s 1 days work = 10299

(A + B)’s 1 day’s work = (123 + 10299) = 23299 = 113

∴ A and B together can complete the job in 13 days.

2. A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ?
(a) 30 days
(b) 15 days
(c) 45 days
(d) 24 days
(e) None of these
Ans.c

Let C completes the work in x days.

Work done by (A + B) in 1 day = 110

Work done by (B + C) in 1 day = 118

A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’work = 1

or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1

or 510 + 518 + 10x = 1 or x = 45 days

3. 12 men complete a work in 18 days. Six days after they had started working, 4 men joined them. How many days will all of them take to complete the remaining work ?
(a) 10 days
(b) 12 days
(c) 15 days
(d) 9 days
(e) None of these
Ans.d

In 1 day, work done by 12 men = 118

In 6 days, work done by 12 men = 618 = 13

Remaining work = 23

m1 × d1 × w2 = m2 × d2 × w1

or 12 × 18 × 23 = 16 × d2 × 1

or d2 = \(\frac{4 \times 18 \times 2}{16} = 9 \; days\)

4. A tyre has two punctures. The first puncture along would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat?
(a) 112 minutes
(b) 312 minutes
(c) 335 minutes
(d) 414 minutes
(e) None of these
Ans.c

1 minute’s work of both the punctures = (19 + 16) = 518

So, both the punctures will make the tyre flat in 185 = 335 min.

5. A man, a woman or a boy can do a job in 20 days, 30 days or 60 days respectively. How many boys must assist 2 men and 8 women to do the work in 2 days?
(a) 15 boys
(b) 8 boys
(c) 10 boys
(d) 11 boys
(e) None of these
Ans.b

Man’s two day’s work = 2 × 120 th work = 110 th work

Woman’s two days’s work

= 2 × 130 th work = 115 th work

Boy’s two day’s work = 2 × 160 th work = 130 th work

Now, let 2 men, 8 women and x boys can complete work in 2 days. Then ,

2 men’s work + 8 women’s work + x boy’s work = 1

2(110) + 8(115) + x(130) = 1

⇒ x = (1 - 15 - 815) × 30 ⇒ x = 8 boys

6. A can do 50% more work as B can do in the same time. B alone can do a piece of work in 20 hours. A, with help of B, can finish the same work in how many hours ?
(a) 12
(b) 8
(c) 1313
(d) 512
(e) None of these
Ans.b

B alone can do a work in 20 hours.

∴ A alone can do 32 of the work in 20 hours.

i.e., A alone can do the same work in 403 hours

∴ (A + B)’s one hour’s work = 340 + 120 = 540 = 18

⇒ A and B together can finish the whole work in 8 hours.

7. If 15 women or 10 men can complete a project in 55 days, in how many days will 5 women and 4 men working together complete the same project ?
(a) 75
(b) 8
(c) 9
(d) 85
(e) None of these
Ans.a

15 W = 10 M

Now, 5W + 4M = 5W + \(\frac{4 \times 15}{10}W\) = 5W + 6W = = 11 W

If 15 women can complete the project in 55 days,
11 women can complete the same project in

\(\frac{55 \times 15}{11} = 75 \; days\)
8. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?
(a) 11 : 30 am
(b) 12 noon
(c) 12 : 30 pm
(d) 1 pm
(e) None of these
Ans.d

(P + Q + R)’s 1 hour’s work = (18 + 110 + 112) = 37120

Work done by P, Q and R in 2 hours = (37120 × 2) = 3760

Remaining work = (1 - 3760) = 2360

(Q + R)’s 1 hour’s work = (110 + 112) = 1160

Now, 1160 work is done by Q and R in 1 hour.

So, 2360 work will be done by Q and R in

(6011 × 2360) = 2311 hours ≈ 2 hours.

So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m.

9. 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?
(a) 6
(b) 613
(c) 623
(d) 723
(e) None of these
Ans.c

10 men’s 1 day’s work = 115

15 women’s 1 day’s work = 112

(10 men + 15 women)’s 1 day’s work

= (115 + 112) = 960 = 320

∴ 10 men and 15 women will complete the work in 203 = 623 days.

10. A can do a piece of work in 10 days, while B alone can do it in 15 days. They work together for 5 days and the rest of the work is done by C in 2 days. If they get 450 for the whole work, how should they divide the money ?
(a) 225, 150, 75
(b) 250, 100, 100
(c) 200, 150, 100
(d) 175, 175, 100
(e) None of these
Ans.a

Work done by A and B in 5 days = (110 + 115) × 5 = 56

Work remaining = 1 - 56 = 16

∴ C alone can do the work in 6 × 2 = 12 days

Ratio of their share work = 510 : 515 : 212 = 3 : 2 : 1

Share of wages = 225, 150, 75.