# TIME AND WORK --1 TO 10

Q. 1. A completes a work in 12 days and B complete the same work in 24
days. If both of them work together, then the number of days required to
complete the work will be

(a) 8 (b) 6 (c) 7 (d) 5 (e) None of these

Ans: (a) 8

Explanation:

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Therefore, here, the required number of days = 12 × 24/ 36 = 8 days. Ans.

Q. 2. If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in

(a) 1 day (b) 1 ½ days (c) ¾ day (d) ½ day (e) None of these

Ans: (a) 1 day

Explanation:

The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m

No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. Ans.

Q. 3. If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in

(a) 7 days (b) 6 days (c) 4 days (d) 3 days (e) None of these

Ans: (d) 3 days.

Explanation:

That is, 1 person can do one time of the work in 3 days.

Therefore, 7 persons can do 7 times work in the same 3 days itself. Ans.

Q. 4. Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is

(a) 15 (b) 10 (c) 9 (d) 8 (e) None of these

Ans: ( d) 8

Explanation:

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

That is, the required No. of days = 10 × 40/50 = 8 days. Ans.

Q. 5. 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required

(a) 4 (b) 5 (c) 6 (d) 8 (e) None of these

Ans: (d) 8

Explanation:

That is, 1 work done = 12 × 8 × 10

Then, 12 8 × 10 = ? × 15 × 8

? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days. Ans.

Q. 6. If 5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in

(a) 25 days (b) 20 days (c) 15 days (d) 10 days (e) None of these

Ans: (a) 25 days

Explanation:

That is, half the work done = 5 × 15 × ½

Then, 5 × 15 × ½ = 3 × ? ×1/2

i.e. 5 × 15 = 3 × ?

therefore, ? (No. days required) = 5 × 15/3 = 25 days. Ans.

Q. 7. 30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers required to finish the same piece of work in 30 days will be

(a) 15 (b) 21 (c) 25 (d) 22 (e) None of these

Ans: (b) 21

Explanation:

That is, 1 work done = 30 × 7 ×18 = ? × 6 × 30

? (No. of labourers) = 30 × 7 × 18/6 × 30

= 21. Ans.

Q. 8. If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be

(a) 20 days (b) 10 days (c) 14 days (d) 15 days (e) None of days

Ans: (d) 15 days

Explanation:

That is, 5 × 9 = 3 × ?

? = 5 × 9/3 = 15 days. Ans.

Q. 9. A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field?

(a) 10 hours (b) 20 hours (c) 30 hours (d) 40 hours (e) None of these

Ans: (c) 30 hours

Explanation:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.

Therefore, the No. of hours required by B = 10 × 15/ 15 – 10 = 150/5 = 30 hours. Ans.

Q. 10. 16 men or 20 women can finish a work in 25 days. How many days 28 men and 15 women will take to finish this job?

(a) 19 13/43 days (b) 11 27/43 days (c) 8 days (d) 10 days (e) None of these

Ans: (d) 10 days

Explanation:

16 men = 20 women

Therefore, 1 women = 16/20 men = 4/5 men

15 women = 4/5 × 15 men = 12 men

i.e. 28 men + 15 women = 28 men + 12 men = 40men

1 work done by men = 16 × 25

16 × 25 = 40 × ?

? ( no. of days) = 16 × 25/40 = 10 days. Ans.

(a) 8 (b) 6 (c) 7 (d) 5 (e) None of these

Ans: (a) 8

Explanation:

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Therefore, here, the required number of days = 12 × 24/ 36 = 8 days. Ans.

Q. 2. If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in

(a) 1 day (b) 1 ½ days (c) ¾ day (d) ½ day (e) None of these

Ans: (a) 1 day

Explanation:

The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m

No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. Ans.

Q. 3. If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in

(a) 7 days (b) 6 days (c) 4 days (d) 3 days (e) None of these

Ans: (d) 3 days.

Explanation:

That is, 1 person can do one time of the work in 3 days.

Therefore, 7 persons can do 7 times work in the same 3 days itself. Ans.

Q. 4. Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is

(a) 15 (b) 10 (c) 9 (d) 8 (e) None of these

Ans: ( d) 8

Explanation:

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

That is, the required No. of days = 10 × 40/50 = 8 days. Ans.

Q. 5. 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required

(a) 4 (b) 5 (c) 6 (d) 8 (e) None of these

Ans: (d) 8

Explanation:

That is, 1 work done = 12 × 8 × 10

Then, 12 8 × 10 = ? × 15 × 8

? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days. Ans.

Q. 6. If 5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in

(a) 25 days (b) 20 days (c) 15 days (d) 10 days (e) None of these

Ans: (a) 25 days

Explanation:

That is, half the work done = 5 × 15 × ½

Then, 5 × 15 × ½ = 3 × ? ×1/2

i.e. 5 × 15 = 3 × ?

therefore, ? (No. days required) = 5 × 15/3 = 25 days. Ans.

Q. 7. 30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers required to finish the same piece of work in 30 days will be

(a) 15 (b) 21 (c) 25 (d) 22 (e) None of these

Ans: (b) 21

Explanation:

That is, 1 work done = 30 × 7 ×18 = ? × 6 × 30

? (No. of labourers) = 30 × 7 × 18/6 × 30

= 21. Ans.

Q. 8. If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be

(a) 20 days (b) 10 days (c) 14 days (d) 15 days (e) None of days

Ans: (d) 15 days

Explanation:

That is, 5 × 9 = 3 × ?

? = 5 × 9/3 = 15 days. Ans.

Q. 9. A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field?

(a) 10 hours (b) 20 hours (c) 30 hours (d) 40 hours (e) None of these

Ans: (c) 30 hours

Explanation:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.

Therefore, the No. of hours required by B = 10 × 15/ 15 – 10 = 150/5 = 30 hours. Ans.

Q. 10. 16 men or 20 women can finish a work in 25 days. How many days 28 men and 15 women will take to finish this job?

(a) 19 13/43 days (b) 11 27/43 days (c) 8 days (d) 10 days (e) None of these

Ans: (d) 10 days

Explanation:

16 men = 20 women

Therefore, 1 women = 16/20 men = 4/5 men

15 women = 4/5 × 15 men = 12 men

i.e. 28 men + 15 women = 28 men + 12 men = 40men

1 work done by men = 16 × 25

16 × 25 = 40 × ?

? ( no. of days) = 16 × 25/40 = 10 days. Ans.

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