Question 1

If 10 spiders can catch 10 files in 10 min, then how many flies can 200 spiders catch in 200 min?

Accepted Answer

Let the required number of flies be N. More spiders, More flies (Direct proportion) More time, More flies (Direct proportion) ∴ 10 x 10 x N = 200 x 200 x 10 ∴ N = (200 x 200 x 10)/(10 x 10) = 4000 flies

Question 2

2000 sodiers in a fort had enough food for 20 days. But some soldiers were transferred to another fort and the food lasted for 25 days. How many soldiers were transferred?

Accepted Answer

Let the number of soldiers transferred be N Now, the food would last for 25 days for (2000 - N) soldiers. Less men, More days (indirect proportion) 25 : 20 : : 2000 : (2000 - N) ⇒ 2000 - N = (2000 x 20)/25 ⇒ 2000 - N = 1600 ∴ N = 2000 - 1600 = 400

Question 3

If in a hostel, food is available for 45 days for 50 students. For how many soldiers for 75 students?

Accepted Answer

∵ For 50 students, food is sufficient for 45 days. ∴ For 1 students, food is sufficient for 45 x 50 days. ∴ For 75 students, food is sufficient for (45 x 50)/75 days i.e., for 30 days .

Question 4

A garrison is provided with ration for 72 soldiers to last for 54 days. Find how long would the same amount of food last for 90 soldiers, if the individual ration is reduced by 10 %?

Accepted Answer

Let the required number of days be N. More men, Less days (indirect proportions) Soldiers 90 : 72 Ratio 9 : 10 N = (72 x 54 x 10)/(90 x 9) = 48 days

Question 5

3 men can do a piece of work in 18 days. 6 boys can also do the same work in 18 days. In how many days, 4 men and 4 boys together will finish the work?

Accepted Answer

3 men ≡ 6 boys ⇒ 1 man ≡ 2 boys ∴ 4 men + 4 boys ≡ 4 men + 2 men = 6 men ∵ 3 men can do a work in 18 days. ∴ 1 man can do a work in 18 x 3 days. ∴ Required number of days = (18 x 3)/6 = 9 days

Question 6

10 men and 8 women can together complete a work in 5 days. Work done by a women is equal to the half of the work done by a man. In how many days, will 4 men and 6 women complete that work?

Accepted Answer

1 women ≡ 1/2 man 10 men + 8 women ≡ 10 men + 4 men = 14 men 4 men + 6 women ≡ 4 men + 3 men = 7 men More men, Less days (Indirect proportion) 7 : 14 : : 5 : N ∴ N = (14 x 5)/7 = 10 days

Question 7

8 men can complete a work in 12 days, 4 women can complete it in 48 days and 10 children can complete the same work in 24 days. In how many days can 10 men, 4 women and 10 children complete the same work?

Accepted Answer

1 man can finish the work in (8 x 12) = 96 days 1 woman can finish the work in (4 x 48) = 192 days 1 child can finish the work in (10 x 24) = 240 days 1 man's 1 day's work = 1/96 1 women's 1 day's work = 1/192 1 child's 1 day's work = 1/240 (10 men + 4 women + 10 children)'s 1 day's work = (10/96 + 4/192 + 10/240) = (5/48 + 1/48 + 1/24) = (5 + 1 + 2)/48) = 8/48 = 1/6 Hence, they will finish the work in 6 days.

Question 8

20 men complete one-third of a work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days?

Accepted Answer

Work done = 1/3 Remaining work = 1 - (1/3) = 2/3 Let the number of more men to be employed be N. More work, More men (Direct proportion) More days, Less men (Indirect proportion) Work 1/3 : 2/3 Days 25 : 20 ∴ 1/3 x 25 x (20 + N) = 2/3 x 20 x 20 ⇒ (20 + N) = 800/25 = 32 ∴ N = 32 - 20 = 12

Question 9

40 men complete one-third of a work in 40 days. How many more men should be employed to finish the rest of the work in 50 more days?

Accepted Answer

Work done = 1/3 Remaining work = (1 - 1/3) = 2/3 Let the number of additional men be N. (Direct proportion) More days, Less men (Indirect proportion) Work 1/3 : 2/3 Days 50 : 40 ∴ 1/3 x 50 x (40 + N) = 2/3 x 40 x 40 ⇒ 5 x (40 + N) = 2 x 40 x 4 ⇒ 200 + 5N = 320 ⇒ 5N = 320 - 200 = 120 ∴ N = 120/5 = 24 ∴ Required number of men = 24

Question 10

If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?

Accepted Answer

7 spiders make 7 webs in 7 days. ∴ 1 spiders make 7 webs in 7 x 7 days. ∴ 1 spiders make 1 webs in 7 x 7 / 7 days. ∴ 1 spiders make 1 webs in 7 days.

Question 11

If 16 men working 7 hours day can plough a field in 48 days, in how many days will 14 men working 12 hours a clay plough the same field?

Accepted Answer

16 men working 7 hours day can plough a field in 48 days. 1 men working 7 hours day can plough a field in 48 x 16 days. 1 men working 1 hours day can plough a field in 48 x 16 x 7 days. 14 men working 1 hours day can plough a field in 48 x 16 x 7 / 14 days. 14 men working 12 hours day can plough a field in 48 x 16 x 7 / 14 x 12 days. 14 men working 12 hours day can plough a field in 48 x 16 / 2 x 12 days. 14 men working 12 hours day can plough a field in 48 x 4 / 2 x 3 days. 14 men working 12 hours day can plough a field in 48 x 2 / 3 days. 14 men working 12 hours day can plough a field in 16 x 2 = 32 days.

Question 12

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Accepted Answer

As per given question, In 1 minute, 6 identical machines can produce a total of 270 bottles. In 1 minute, 1 identical machines can produce a total of 270 / 6 bottles. In 1 minute, 10 identical machines can produce a total of 270 x 10 / 6 bottles. In 4 minute, 10 identical machines can produce a total of 270 x 10 x 4 / 6 bottles. In 4 minute, 10 identical machines can produce a total of 45 x 10 x 4 bottles. In 4 minute, 10 identical machines can produce a total of 1800 bottles.

Question 13

If the price of 357 apples is Rs. 1517.25, what will be the approximate price of 49 dozens of such apples?

Accepted Answer

As we know that, 1 Dozen = 12 piece 49 Dozen = 49 x 12 piece Price of 357 apples is Rs. 1517.25. Price of 1 apples is Rs. 1517.25 / 357. Price of 49 x 12 apples is Rs. 1517.25 x 49 x 12 / 357. Price of 49 x 12 apples is Rs. 1517.25 x 7 x 12 / 51. Price of 49 x 12 apples is Rs. 1517.25 x 7 x 4 / 17. Price of 49 x 12 apples is Rs. 2499. So Price will be around 2500 and answer will be 2500.

Question 14

On a scale of a map 0.6 cm represents 6.6 km. If the distance between two points on the map is 80.5 cm, what is the actual distance between these points?

Accepted Answer

0.6 cm represents 6.6 km in a scale. 1 cm represents 6.6 / 0.6 km in a scale. 80.5 cm represents 6.6 x 80.5 / 0.6 km in a scale. 80.5 cm represents 11 x 80.5 km in a scale. 80.5 cm represents 885.5 km in a scale.

Question 15

8 persons can build a wall 140 m long in 42 days. In how many days can 30 persons complete a similar wall 100 m long?

Accepted Answer

As per given question, 8 persons can build a wall 140 meter long in 42 days. 1 persons can build a wall 140 meter long in 42 x 8 days. 1 persons can build a wall 1 meter long in 42 x 8 / 140 days. 30 persons can build a wall 1 meter long in 42 x 8 / 30 x 140 days. 30 persons can build a wall 100 meter long in 42 x 8 x 100 / 30 x 140 days. 30 persons can build a wall 100 meter long in 42 x 8 / 3 x 14 days. 30 persons can build a wall 100 meter long in 42 x 8 / 42 days. 30 persons can build a wall 100 meter long in 8 days.

Question 16

A certain number of persons can finish a piece of work in 100 days . If there were 10 persons less, it would take 10 more days finish the work. How many persons were there originally?

Accepted Answer

Given in the question, Let y be the persons there originally . Work done by y persons can finish = 100 days If there were 10 persons less, it would take more days finish the work in 10 days i.e. ( y - 10 ) = 110 According to question , y × 100 = ( y - 10 ) × 110 ⇒ 100y = 110y - 1100 ⇒ 10y = 1100 ⇒ y = 110 Therefore , 110 persons were there originally .

Question 17

A garrison of 500 persons had provisions for 27 days. After 3 days a reinforcement of 300 persons arrived. For how many more days will the remaining food last now?

Accepted Answer

Let the remaining food will last for D days. 500 men had provisions for (27 − 3) = 24 days. ( 500 + 300 ) men had provisions for D days. More men, Less days ( Indirect Proportion ) we can write as :- ∴ 800 : 500 :: 24 : x ⇔ (800 × D ) =( 500 × 24 ) ⇔ ( 500 × 24 ) /800 =15 Therefore , 15 days is correct answer .

Question 18

A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?

Accepted Answer

Suppose the food will last for D days at same rate . 250 men had provisions for 40 days. ( 250 - 50 ) men had provisions for D days. Less men, More days ( Indirect Proportion ) we can write as :- ∴ 200 : 250 :: 40 : D ⇔ (200 × D ) =( 250 × 40 ) ⇔ ( 250 × 40 ) /200 = 50 Therefore , 50 days is required answer .

Question 19

In a camp, food was sufficient for 2000 people for 54 days. After 15 days, more people came and the food last only for 20 more days. How many people came?

Accepted Answer

Question 20

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

Accepted Answer

According to question , 3 pumps working in 2 days = 8 × 2 = 16 hours It means that they can empty a tank in 16 hours . 3 pumps 1 hour work = 1/16 1 pumps 1 hour work = 1/( 3 × 16 ) 4 pumps 1 hour work =4 × 1/( 3 × 16 ) = 1 / 12 Hence , they will empty the tank in 12 hours .

Unitary Method Questions