Question 1

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

Accepted Answer

Let us assume that each soldier eats one unit of food per day. Thus, total units of food at the beginning will be 1000 x 30 = 30000. After 10 days 1000 soldiers would have eaten 1000 x 10 = 10000 units of food. Thus food left after 10 days equals 20000 units. Now, there are total of 2000 soldiers who eat one unit of food every day. So, the number of days that 20000 units of food will serve 2000 soldiers is 20000/2000 = 10

Question 2

A man and a boy working together can complete a work in 24 days. If for the last 6 days, the man alone does the work, then it is completed in 26 days. How long will the boy take to complete the work alone?

Accepted Answer

Let man's 1 day's work = 1/m and boy's 1 day's work = 1/n 1 day's work man and boy = 1/24 Man's 6 day's work = 6/m Now, for 20 days, both man and boy do the work and for last 6 days, only man does the work. According to the question, 1/m + 1/n = 1/24 ⇒ 20(1/m + 1/n) + 6/m = 1 ⇒ 20 x (1/24) + 6/m = 1 ⇒ 6/m = (1 - 20/24) = 4/24 = 1/6 ⇒ 1/n = 1/36 Now from eq. (i) 1/m + 1/n = 1/24 1/36 + 1/n = 1/24 ⇒ 1/n = (1/24) - (1/36) = 1/72 Hence, the boy alone can do the work in 72 days.

Question 3

25 men can reap a field in 20 days. when should 15 men leave the work, if the whole field is to be reaped in 37 1/ 2 days after they leave the work?

Accepted Answer

Let 15 men work for m days. Work done in 1 days = m/20 Remaining work = (1 - m/20) 25 men's 1 days work = 1/20 1 man's 1 days work = (1/20) x (1/25) = 1/500 10 men's 1 days work = 10/500 = 1/50 10 men's 75/2 days work = (1/50) x (75/2) = 75/100 = 3/4 ∴ (1 - m/20) = 3/4 ⇒ m/20 = 1/4 ⇒ m = (1/4) x 20 = 5 Clearly, 15 men leave after 5 days.

Question 4

If 12 men or 18 women can do a piece of work in 14 days, then how long will 8 men and 16 women take to finish the work?

Accepted Answer

12 men ≡ 18 women ⇒ 1 man ≡ 18/12 women ≡ 3/2 women ∴ 8 men ≡ (3/2) x 8 = 12 women ∴ 8 men + 16 women = 12 women + 16 women = 28 women ∵ 18 women can do the work in 14 days . ∴ 1 woman can do the same work in (14 x 18) days. ∴ 28 women will do the same work in (14 x 18)/28 days. ∴ Required number of days = (14 x 18)/28 = 9 days

Question 5

When a 192 meters long rod is cut down into small pieces of length 3·2 meters each. Then how many pieces are available?

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Question 6

The cost of 2 tables is equal to the cost of 5 chairs. If the difference of the cost of one table and one chair is Rs. 1200, then the cost of one chair is —

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Question 7

If the cost of 1/4 th of kg is Rs. 0·60, then what is the cost of 200 gm ?

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Question 8

If the cost of 3 dozens mangoes is Rs. 245, what will be the approximate cost of 363 mangoes?

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Question 9

If the weight of 13 meters long rod is 23·4 kg. What is the weight of 6 meters long rod?

Accepted Answer

Question 10

357 mangoes cost Rs. 1517·25, then what is the approximate cost of 49 dozen of mangoes?

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Question 11

Cost of 7000 bricks is Rs. 5740. Cost of luggage to carry the bricks to the building place is Rs. 805. What is the cost at per thousand bricks?

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Question 12

5 dozen toys are packed in a box and 98 boxes are kept in a tempo. How many tempos can lift 29400 toys in one round?

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Question 13

Cost of 1 dozen of bananas is Rs. 2·35, then what is the 4 approximate cost of 42 dozen of bananas?

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Question 14

Cost of 1 chair is Rs. 214 and cost of one table is Rs. 937, then what is the approximate cost of 6 dozen chairs and 4 dozen tables?

Accepted Answer

Here , Cost of 1 chair = Rs. 214 and cost of one table = Rs. 937 . ∵ Cost of 6 dozen chairs = 6 × 12 × 214 = Rs. 15408 and cost of 4 dozen tables = 4 × 12 × 937 = Rs. 44976 ∴ Total cost = 15408 + 44976 Total cost = Rs. 15408 + 44976 = Rs. 60384 Total cost of chairs and tables ≅ Rs. 60000 (Approximately)

Question 15

3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?

Accepted Answer

3 pumps, can empty a tank in 2 days by working 8 hours a day. 1 pumps, can empty a tank in 2 days by working 8 x 3 hours a day. 1 pumps, can empty a tank in 1 days by working 8 x 3 x 2hours a day. 4 pumps, can empty a tank in 1 days by working 8 x 3 x 2 / 4 hours a day. 4 pumps, can empty a tank in 1 days by working 2 x 3 x 2 hours a day. 4 pumps, can empty a tank in 1 days by working 12 hours a day.

Question 16

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

Accepted Answer

39 persons can repair a road by working 5 hours a day in 12 days. 1 persons can repair a road by working 5 hours a day in 12 x 39 days. 1 persons can repair a road by working 1 hours a day in 12 x 39 x 5 days. 30 persons can repair a road by working 1 hours a day in 12 x 39 x 5 / 30 days. 30 persons can repair a road by working 6 hours a day in 12 x 39 x 5 / 30 x 6 days. 30 persons can repair a road by working 6 hours a day in 2 x 39 x 5 / 30 days. 30 persons can repair a road by working 6 hours a day in 39 x 1 / 3 days. 30 persons can repair a road by working 6 hours a day in 13 days.

Question 17

A contract is to be completed in 56 days if 104 persons work, each working at 8 hours a day. After 30 days, 25 % of the work is completed. How many additional persons should be deployed so that the work will be completed in the scheduled time, each …

Accepted Answer

According to question ,

Question 18

'P' men working 'P' hours per day can do 'P' units of a work in 'P' days. How much work can be completed by 'Q' men working 'Q' hours per day in 'Q' days?

Accepted Answer

As we know from the given question, P men working P hours per day in P days can do P units of a work. 1 men working P hours per day in P days can do P / P units of a work. 1 men working 1 hours per day in P days can do P /P x P units of a work. 1 men working 1 hours per day in 1 days can do P /P x P x P units of a work. Q men working 1 hours per day in 1 days can do P x Q /P x P x P units of a work. Q men working Q hours per day in 1 days can do P x Q x Q /P x P x P units of a work. Q men working Q hours per day in Q days can do P x Q x Q x Q/P x P x P units of a work. Q men working Q hours per day in Q days can do Q3/P2 units of a work.

Question 19

In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

Accepted Answer

Question 20

10 men, working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days?

Accepted Answer

Unitary Method Questions