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Three men, four women, and six children can complete a work in 9 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 9 days?

A.

7

B.

8

C.

9

D.

6

Answer with explanation

Answer: Option AExplanation

OR

A woman does double the work a man does i.e., W = 2M

the child does half the work a man does i.e., C = M/2

Thus, C = M/2

==> C = [W/2]/2 i.e., W = 2M ==> M = W/2

==> C = W/4

Now, three men, four women, and six children

= 3W/2 + 4W + 6W/4

= 3W/2 + 4W + 3W/2

= (3W + 8W + 3W)/2 (L.C.M)

= 14W/2

= 7W

Hence, 7 women complete the work in 9 days.

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A laborer is engaged for 30 days on the condition that he receives Rs.25 for each day he works and is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent ?

A.

10 days

B.

14 days

C.

11 days

D.

9 days

Answer with explanation

Answer: Option AExplanation

For 30 days he receives

30 x 25 = 750

Actually he gets 425

Therefore, Fine is 750 – 425 = 325

=> No of days absent = 325/(25+7.50)= 10

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Two boys and a girl can do a work in 5 days, while a boy and 2 girls can do it in 6 days. If the boy is paid at the rate of 28$ a week, what should be the wages of the girl a week ?

A.

24 $

B.

22 $

C.

16 $

D.

14 $

Answer with explanation

Answer: Option CExplanation

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If 6 engines consume 24 metric tonnes of coal, when each is working 8 hours day, how much coal will be required for 9 engines, each running 13hours a day, it being given that 2 engines of former type consume as much as 3 engines of latter type ?

A.

45 metric tonnes

B.

47 metric tonnes

C.

55 metric tonnes

D.

34 metric tonnes

Answer with explanation

Answer: Option AExplanation

2 engines of former type for one hour consumes (2 x 24)/(6 x8) = 1 metric ton

i.e. 3 engines of latter type consumes 1 ton for one hour

Hence 9 engines consumes 3 tons for one hour

For 15 hours it is 15 x 3 = 45 metric tonnes.

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A group of men can complete a job in K hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of K ?

A.

7 hrs

B.

7.5 hrs

C.

8 hrs

D.

8.25 hrs

Answer with explanation

Answer: Option BExplanation

Let there are L men

job requires LK man hours.

job completed in first 4 hrs = L x 4 = 4L

job completed in next 4 hrs = 4 x L/2 = 2L

job completed in next 4 hrs = 4 x L/4 = L

job completed in last 4 hrs = 4 x L/8 = L/2

4L + 2L + L + L/2 = KL

K = 7+1/2 = 7.5 hours.

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A.

10

B.

5

C.

4

D.

13

Answer with explanation

Answer: Option BExplanation

Since 20% i.e 1/5 typists left the job. So, there can be any value which is multiple of 5 i.e, whose 20% is always an integer. Hence, 5 is the least possible value.

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In a hostel, there was food for 1000 students for one month. After 10 days, 1000 more students joined the hostel. How long would the students be able to carry on with the remaining food?

A.

10 days

B.

15 days

C.

20 days

D.

5 days

Answer with explanation

Answer: Option AExplanation

After 10 days, the remaining food would be sufficient for the 1000 students for 20 more days

–>If 1000 more students are added, it shall be sufficient for only 10 days (as the no. of students is doubled, the days are halved).

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hree taps P, Q and R can fill a tank in 12 hrs, 15 hrs and 20 hrs respectively. If P is open all the time and Q and R are open for one hour each alternately, starting with Q, then the tank will be full in how many hours ?

A.

9 hrs

B.

7 hrs

C.

13 hrs

D.

11 hrs

Answer with explanation

Answer: Option BExplanation

Given,

P can fill in 12 hrs

Q can fill in 15 hrs

R can fill in 20 hrs

=> Volume of tank = LCM of 12, 15, 20 = 60 lit

=> P alone can fill the tank in 60/12 = 5 hrs

=> Q alone can fill the tank in 60/15 = 4 hrs

=> R alone can fill the tank in 60/20 = 3 hrs

Tank can be filled in the way that

(P+Q) + (P+R) + (P+Q) + (P+R) + ….

=> Tank filled in 2 hrs = (5+4) + (5+3) = 9 + 8 = 17 lit

=> In 6 hrs = 17 x 6/2 = 51 lit

=> In 7th hr = 51 + (5+4) = 51 + 9 = 60 lit

=> So, total tank will be filled in **7 hrs**.

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Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work ?

A.

18 days

B.

20 days

C.

16 days

D.

14 days

Answer with explanation

Answer: Option BExplanation

(5m + 9w)10 = (6m + 12w)8

=> 50m + 90w = 48w + 96 w => 1m = 3w

5m + 9w = 5m + 3m = 8m

8 men can do the work in 10 days.

3m +3w = 3m + 1w = 4m

So, 4 men can do the work in (10 x 8)/4 = 20 days.

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**A** can build a wall in 16 days while **B** can destroy it in 8 days.** A**worked for 5 days. Then** B** joined with** A** for the next 2 days. Find in how many days could **A** build the remaining wall ?

A.

12 days

B.

14 days

C.

13 days

D.

16 days

Answer with explanation

Answer: Option CExplanation

Now, Total work = LCM(16, 8) = 48

A’s one day work = + 48/16 = + 3

B’s one day work = – 48/8 = -6

Given A worked for 5 days to build the wall => 5 days work = 5 x 3 = + 15

2days B joined with A in working = 2(3 – 6) = – 6

Remaining Work of building wall = 48 – (15 – 6) = 39

Now this remaining work will be done by A in = 39/3 = 13 days.

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Twenty men can do a work in eighteen days. Eighteen women can complete the same work in fifteen days. What is the ratio between the capacity of a woman and a man ?

A.

4:5

B.

3:4

C.

4:3

D.

2:3

Answer with explanation

Answer: Option CExplanation

(20 x 18) men can complete the work in in one day.

one man’s one day work = 1/360

(18 x 15) women can complete the work in 1 day

1 woman’s one day work = 1/270

So, required ratio = 1/270:1/360= 4:3

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