**1. **‘x’ number of men can finish a piece

of work in 30** **days. If there were 6

men more, the work could be finished in 10 days less. The actual number of men

is:

(a) 6

(b) 10

(c) 12

**2.**8 men can complete a piece of work in

20 days. 8 women can complete the same work in 32 days. In how many days will 5

men and 8 women together complete the same work?

(a) 16 days

(b) 12 days

(c) 14 days

**4.**15 Men take 20

days to complete a job working 8 hours a day. The number of hours a day should

20 men take to complete the job in 12 days is:

(a) 5 hours

(b) 10 hours

(c) 15 hours

**5.**3 persons undertake to complete a

piece of work for Rs. 1,200. The first person can complete the work in 8 days,

second person in 12 days and third person in 16 days. They complete the work

with the help of a fourth person in 3 days. What does the fourth person get?

(a) Rs. 180

(b) Rs. 200

(c) Rs. 225

(d) Rs. 250

Sol. Let the fourth person complete the entire work in x days.

Now, according to the question:

3/8+3/12+3/16+3/x=1

⇒1/x=1/3-1/8-1/12-1/16=(16 – 6 – 4 – 3)/48=1/16

∴ x = 16

Ratio of wages =1/8 ∶1/12 ∶1/16 ∶1/16=6∶4∶3∶3

Sum of ratios = 6 + 4 + 3 + 3

∴ Fourth person’s share =3/16×1200 =Rs. 225.

Sol. Let the fourth person complete the entire work in x days.

Now, according to the question:

3/8+3/12+3/16+3/x=1

⇒1/x=1/3-1/8-1/12-1/16=(16 – 6 – 4 – 3)/48=1/16

∴ x = 16

Ratio of wages =1/8 ∶1/12 ∶1/16 ∶1/16=6∶4∶3∶3

Sum of ratios = 6 + 4 + 3 + 3

∴ Fourth person’s share =3/16×1200 =Rs. 225.

**7.**A can do a piece

of work in 20 days and B in 30 days. They work together for 7 days and then

both leave the work. Then C alone finishes the remaining work in 10 days. In

how many will C finish the full work?

(a) 25 days

(b) 30 days

(c) 24 days

(d) 20 days

Sol.(c) Work done by A and B in 7 days

=7/20+7/30=(21+14)/60=35/60=7/12

Remaining work =1-7/12=5/12

∴ Time taken by C =12/5×10= 24 days

Sol.(c) Work done by A and B in 7 days

=7/20+7/30=(21+14)/60=35/60=7/12

Remaining work =1-7/12=5/12

∴ Time taken by C =12/5×10= 24 days

**9.**A farmer can

plough a filed working 6 hours per day in 18 days. The worker has to work how

many hours per day to finish the same work in 12 days?

(a) 7

(b) 9

(c) 11

**10.**A does 1/5 of a work in a week. B finishes the work in 15

Days. B starts the work and works only for 3 days. Thereafter A completes the

job. He will finish it in:

(a) 10 days

(b) 7 days

(c) 12 days

(d) 28 days

Sol.(d) Time taken by A in doing the work = 35 days

Time taken by B in doing the same work = 15 days

B’s 3 days’ work =3/15=1/5

Remaining work =1-1/5=4/5

∴ Time taken by A in finishing the remaining work =(35×4/5)=28 days

Time taken by B in doing the same work = 15 days

B’s 3 days’ work =3/15=1/5

Remaining work =1-1/5=4/5

∴ Time taken by A in finishing the remaining work =(35×4/5)=28 days

**12.**2 men and 4 boys

can do a piece of work in 10 days, while 4 men and 5 boys can do it in 6 days.

Men and boys are paid wages according to their output. If the daily wage of a

man is Rs. 40, then the ratio of daily wages of a man and a boy will be:

(a) 5 : 3

(b) 5 : 2

(c) 7 : 4

(d) 7 : 3

Sol.(b) (2m+4b)×10=(4m+5b)×6

⇒20m+40b=24m+30b

⇒4m=10b

⇒2m=5b

∴5b=2×40

⇒b=(2×40)/5=16

∴ required ratio = 40 : 16 = 5 : 2

⇒20m+40b=24m+30b

⇒4m=10b

⇒2m=5b

∴5b=2×40

⇒b=(2×40)/5=16

∴ required ratio = 40 : 16 = 5 : 2

**14.**P, Q, R are

employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q in rupees, is:

(a) 2850

(b) 3750

(c) 2750

(d) 1000

Sol.(d) Work done by (P + Q + R) = 1 …(i)

Work done by (P + Q) =19/23 …(ii)

Work done by (Q + R) =8/23 …(iii)

From equations (ii) + (iii) – (i)

Q =19/23+8/23-1=(27 – 23)/23=4/23

∴ Wages of Q =4/23×5750 = Rs. 1000

Work done by (P + Q) =19/23 …(ii)

Work done by (Q + R) =8/23 …(iii)

From equations (ii) + (iii) – (i)

Q =19/23+8/23-1=(27 – 23)/23=4/23

∴ Wages of Q =4/23×5750 = Rs. 1000

**15.**A and B together can complete a piece

of work in 12 days and B and C together in 15 days. If A is twice as good a

workman as C, then in how many days will B alone complete the same work?

(a) 30

(b) 25

(c) 24