Question 1

A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?

Accepted Answer

A certain industrial loom weaves 0.128 meters of cloth in 1 second. A certain industrial loom weaves 1 meters of cloth in 1/0.128 second. A certain industrial loom weaves 25 meters of cloth in 25 x 1/ 0.128 second. A certain industrial loom weaves 25 meters of cloth in 195.312 second.

Question 2

If 18 binders bind 900 books in 10 days, How many binders will be required to bind 660 books in 12 days?

Accepted Answer

According to given question, Since 900 books are bonded in 10 days by 18 binders. ∴ 1 books are bonded in 10 days by 18 / 900 binders. ∴ 1 books are bonded in 1 days by 18 x 10 / 900 binders. ∴ 660 books are bonded in 1 days by 18 x 10 x 660 / 900 binders. ∴ 660 books are bonded in 12 days by 18 x 10 x 660 / 12 x 900 binders. ∴ 660 books are bonded in 12 days by 18 x 10 x 55 / 900 binders. ∴ 660 books are bonded in 12 days by 18 x 55 / 90 binders. ∴ 660 books are bonded in 12 days by 55 / 5 binders. ∴ 660 books are bonded in 12 days by 11 binders.

Question 3

If the Price of 6 toys is Rs. 264.37, What will be the approximate price (Rs) of 5 toys?

Accepted Answer

Given in the question, Price of 6 toys is Rs. 264.37. ∴ Price of 1 toys is Rs. 264.37/ 6 . ∴ Price of 5 toys is Rs. 264.37 x 5 / 6 . ∴ Price of 5 toys is Rs. 44 x 5 . ∴ Price of 5 toys is Rs. 220.

Question 4

A person works on a project and completes 5/8 of the job in 10 days. At this rate, how many more days will he it take to finish the job?

Accepted Answer

A person completes 5/8 part of the project in 10 days. A person completes the project in 10/5/8 days. A person completes the project in 10 x 8 /5 days. A person completes the project in 2 x 8 days. A person completes the project in 16 days.

Question 5

A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. how many times can it go round a cylinder having radius 20 cm?

Accepted Answer

Given in the question, If radius is 14 cm then rope can make 70 rounds. If radius is 1 cm then rope can make 70 x 14 rounds. If radius is 20 cm then rope can make 70 x 14 / 20 rounds. If radius is 20 cm then rope can make 7 x 7 rounds. If radius is 20 cm then rope can make 49 rounds.

Question 6

A garrison had provisions for a certain number of days. After 10 days, 1 / 5 of the men desert and it is found that the provisions will now last just as long as before. How long was that?

Accepted Answer

Suppose that y men had provisions for D days .Then y men had provisions for ( D - 10 ) days . [ y - ( y/5 ) ] men had provisions for D days . According to question , ∴ y( D - 10 ) = ( 4y/5 ) x D ⇒ 5Dy - 50y = 4Dy ⇒ Dy - 50y = 0 ⇒ y( D - 50 ) = 0 ⇒ D = 50 days Hence required answer is 50 days .

Question 7

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

Accepted Answer

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

Question 8

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

Accepted Answer

Question 9

A flagstaff 17.5 meters high casts a shadow of length 40.25 meters. What will be the height of a building, which casts a shadow of length 28.75 meters under similar conditions?

Accepted Answer

According to question, A shadow of length 40.25 meters is build for a height of 17.5 meters. A shadow of length 1 meters is build for a height of 17.5 /40.25 meters. A shadow of length 28.75 meters is build for a height of 17.5 x 28.75 /40.25 meters. A shadow of length 28.75 meters is build for a height of 17.5 x 2875 /4025 meters. A shadow of length 28.75 meters is build for a height of 17.5 x 575 /805 meters. A shadow of length 28.75 meters is build for a height of 17.5 x 115/161 meters. A shadow of length 28.75 meters is build for a height of 12.5 meters.

Question 10

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

Since 6 identical machines in 1 minute can produce a total of 270 bottles. ∴ 1 identical machines in 1 minute can produce a total of 270 / 6 bottles. ∴ 10 identical machines in 1 minute can produce a total of 270 x 10 / 6 bottles. ∴ 10 identical machines in 4 minute can produce a total of 270 x 10 x 4 / 6 bottles. ∴ 10 identical machines in 4 minute can produce a total of 45 x 10 x 4 bottles. ∴ 10 identical machines in 4 minute can produce a total of 1800 bottles.

Question 11

If in a hostel 45 days, food is available food is available for 50 students, for how many days will this food be sufficient for 75 students?

Accepted Answer

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

Question 12

If price of m articles is ₹ n, then what is the price of 5 articles?

Accepted Answer

∵ Price of m articles = ₹ n ∴ Price of 1 article = ₹ n/m ∴ Price of 5 articles = ₹ 5n/m

Question 13

12 men can do a piece of work in 24 days. How many days are needed to complete the work, if 8 men are engaged in the same work?

Accepted Answer

Let the required number of days be N. Let men, More days (indirect proportion) 8 : 12 : : 24 : N ∴ N = (12 x 24)/8 = 36 days

Question 14

Maganlal, a worker, makes an article in every 2/3h. If he works for 7 1/ 2h, then how many articles will he make?

Accepted Answer

∵ In 2/3h, 1 article is made. ∴ In 1h, 3/2 article are made. ∴ In 71/2 = 15/2h, 3/2 x 15/2 = 45/4 article are made. ∴ Required articles = 45/4 = 112/4

Question 15

Shantanu completes 5/8 of a job in 20 days. At this rate, how many more days will he take to finish the job?

Accepted Answer

Let the required number of days be N. Remaining work = 1 - 5/8 = 3/8 Less work, Less days (Direct proportion) 5/8 : 3/8 : : 20 : N ⇒ N = (3/8) x 20 x 8/5 ∴ N = 12 days

Question 16

20 men can build 56 m long wall in 6 days. What length of a similar wall can be built by 70 men in 3 days?

Accepted Answer

Let the required length be L m. More men, More length (Direct proportion) Less days, Less length (Direct proportion) Men 20 : 70 Days 6 : 3 ∴ (20 x 6 x L) = (70 x 3 x 56) ∴ L = (70 x 3 x 56) / (20 x 6) = 98 m

Question 17

22 men can complete a job in 16 days. In how many days, will 32 men complete that job?

Accepted Answer

∵ 22 men do the work in 16 days. ∴ 1 man will do the work in 16 x 22 days. ∴ 32 men will do the job in = (16 x 22)/32 days ∴ Required number of days = (16 x 22)/32 = 11 days

Question 18

If 30 men working 9 h per day can reap a field in 16 days, in how many days, will 36 men reap the field working 8 h per day?

Accepted Answer

Here M1 = 30, D1 = 16, T1 = 9, M2 = 36 and T2 = 8 By formula, M1D1T1 = M2D2T2 30 x 16 x 9 = 36 x D2 x 8 ∴ D2 = (30 x 16 x 9)/(36 x 8) = 15 days

Question 19

A garrison of 1000 men had provisions for 48 days. However, a reinforcement of 600 men arrived. How long will now food last for?

Accepted Answer

∵ For 1000 men, provision lasts for 48 days. ∴ For 1 men, provision lasts for (48 x 1000) days. ∴ For (1000 + 600) men, provision will last for (48 x 1000)/1600 days. ∴ Required number of days = (48 x 1000)/1600 = 3 x 10 = 30

Question 20

If 12 persons working 16 h per day earn ₹ 33600 per week, then how much will 18 persons earn working 12 h per day?

Accepted Answer

M1 = 12 H1 = 16, W1 = 33600 M2 = 18, H2 = 12, W2 = ? By formula, M1H1/W1 = M2H2/W2 (12 x 16)/33600 = (18 x 12)/W2 ⇒ W2 = (33600 x 18)/16 ⇒ W2 = 2100 x 8 ∴ W2 = 37800

Unitary Method Questions