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Unitary Method Questions | Short/Full Concepts with Solved Examples, PDF

Unitary Method Questions

Unitary Method involves the questions related to distance, time, speed and problems related to finding the cost of things. Here, you will get Unitary Method Questions with Solved Examples as well as the explanation of concepts in short and full way. Also, download the Unitary Method Questions PDF for practice from here.

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What is Unitary Method?

Unitary method is a method in which you find the value of a unit and then the value of a required number of units. For Eg. Suppose the shopkeeper tells you that he is selling 50 apples for Rs 500.In this case, the apples are the units, and the cost of the apples is the value.

Solved Examples of Unitary Method:

Question 1: A car runs 150 km on 15 litres of fuel, how many kilometres will it run on 10 litres of fuel?

Solution: 15 litres = 150 km

1 litre = 150/15 = 10 km

10 litres = 10 x 10 = 100 km

The car will run 100 kilometres on 10 litres of fuel.

Question 2: If 45 students can consume a stock of food in 22 months, then for how many days the same stock of food will last for 27 students?

  1. 100 days
  2. 144 days
  3. 160 days
  4. 180 days

Solution: According to the first condition, students consume food in 2 months, i.e. in 60 days. So this ratio would be 45:60

According to the second condition, the same amount of food is consumed by 27 students in x days. So that ratio would be 27:x. By Inverse Proportion,

45 × 60 = 27 × x

x = (45 × 60) / 27

x = 100

Get Here: Quadratic Equation Formulas, Tricks

Unitary Method in Ratio and Proportion:

Example: Income of Amir is Rs 12000 per month, and that of Amit is Rs 191520 per annum. If the monthly expenditure of each of them is Rs 9960 per month, find the ratio of their savings.

Solution: Savings of Amir per month = Rs (12000 – 9960) = Rs 2040

In 12 month Amit earn = Rs.191520

Income of Amit per month =  Rs 191520/12 = Rs. 15960

Savings of Amit per month = Rs (15960 – 9960) =  Rs 6000

Therefore, the ratio of savings of Amir and Amit  = 2040:6000 = 17:50

Check Out: Important Ratio and Proportion Tricks

Unitary Method Speed Distance Time:

Example: A car travelling at a speed of 140 kmph covers 420 km. How much time will it take to cover 280 km?

Solution: First, we need to find the time required to cover 420 km.

Speed = Distance/Time

140 = 420/T

T = 3 hours

Applying the unitary method,

420 km = 3 hours

1 km = 3/420 hour

280 km = (3/420) x 280 = 2 hours

Know Here: Time and Distance Tricks

Unitary Method For Time and Work:

Example: “A” finishes his work in 15 days while “B” takes 10 days. How many days will the same work be done if they work together?

Solution:

If A takes 15 days to finish his work then,

A’s 1 day of work = 1/15

Similarly, B’s 1 day of work = 1/10

Now, total work is done by A and B in 1 day = 1/15 + 1/10

Taking LCM(15, 10), we have,

1 day’s work of A and B = (2+3)/30

1 day’s work of  (A + B) = ⅙

Thus, A and B can finish the work in 6 days if they work together.

Get Here: Time and Work Tricks

Unitary Method Questions

Unitary Method Questions and Answers

Question 1) If 16 dozens bananas cost Rs. 360, then how many bananas can be bought in Rs. 60 ?

  1. 16 bananas
  2. 48 bananas
  3. 32 bananas
  4. 50 bananas

Answer: (3)

Explanation: Let the required number of bananas be N.
16 dozens bananas = 16 x 12 = 192 bananas
Less bananas, Less cost (Direct proportion)
360 : 60 : : 192 : N
∴ N = (60 x 192)/360 = 32 bananas

Question 2) If cost of 15 eggs is Rs. 75, then find out the cost of 4 dozens eggs.

  1. 240
  2. 300
  3. 150
  4. 185

Answer: (1)

Explanation:

∵ Cost of 15 eggs = Rs. 75

∴ Cost of 1 egg = Rs. 75/15

∴ Cost of 4 dozens (4 x 12) = Cost of 48 eggs

= (75/15) x 48 = Rs. 240

Question 3) If cost of 12 pens is Rs. 84, then what is the cost of 10 such pens ?

  1. 90
  2. 72
  3. 65
  4. 70

Answer: (4)

Explanation:

∵ Cost of 12 pens = Rs. 84

Cost of 1 pen = Rs. 84/12

∴ Cost of 10 pens = (84/12) x 10

= 7 x 10 = Rs. 70

Read Out: Stocks and Shares Concepts

Question 4) If 20 articles cost Rs. 90, then the cost of 9 articles is ?

  1. 45
  2. 40.50
  3. 4.50
  4. None of these

Answer: (2)

Explanation:

Cost of 20 articles = Rs. 90

Cost of 1 article = Rs. 90/20

∴ Cost of 9 article = 9 x 90/20 = Rs. 40.50

Question 5) If cost of 24 oranges is Rs. 72, then find out the cost of 120 oranges.

  1. 180
  2. 360
  3. 172
  4. 500

Answer: (2)

Explanation:

Let the required cost be Rs. N.

More orange, more cost (Direct proportion)

24 : 120 : : 72 : N

∴ N = (120 x 72)/24 = Rs. 360

Question 6) If 45 m of a uniform rod weight 171 kg, then what will be the weight of 12 m of the same rod ?

  1. 49 kg
  2. 5 kg
  3. 55 kg
  4. 6 kg

Answer: (4)

Explanation:

Let the required weight be w kg.

Less length, Less weight (Direct proportion)

45 : 12 :: 171 : w

∴ w = (12 x 171)/45 = 45.6 kg

Check Out: Simplification Questions & Answers

Question 7) A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole ?

  1. 150 m
  2. 200 m
  3. 125 m
  4. 115 m

Answer: (1)

Explanation:

∵ 8 m shadow means original height = 12 m

∴ 1 m shadow means original height = 12/8 m

∴ 100 m shadow means original height = (12/8) x 100 m

= (6/4) x 100 = 6 x 25 = 150 m

Question 8) A worker makes a toy in every 2h. If he works for 80h, then how many toys will he make ?

  1. 40
  2. 54
  3. 45
  4. 39

Answer: (1)

Explanation:

Let number of toys be N.

More hours, More toys (Direct proportion)

2 : 80 : : 1 : N

⇒ N = 80/2 = 40 toys

Know Here: Volume and Surface Area Important Formula

Question 9) In a race , Ravi covers 5 km in 20 min. How much distance will he cover in 100 min ?

  1. 40 km
  2. 35 km
  3. 26 km
  4. 25 km

Answer: (4)

Explanation:

∵ Distance covered in 20 min = 5 km

∴ Distance covered in 1 min = 5/20 km

∴ Distance covered in 100 min = (5/20) x 100

= 5 x 5 = 25 km

Question 10) In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

  1. 15
  2. 40
  3. 38
  4. 32

Answer: (2)

Explanation:

40 cows eat 40 bags of husk in 40 days.

∴ 1 cows eat 40 bags of husk in 40 x 40 days.

∴ 1 cows eat 1 bags of husk in 40 x 40 / 40 days.

∴ 1 cows eat 1 bags of husk in 40 days.

Download: Unitary Method Questions and Answers PDF

All the details about Unitary Method Questions on this page is well written by the team members of recruitmentresult.com Individuals must practice from it to score well in the examination.

Something That You Should Put an Eye On

Time And Distance Questions Ratio and Proportion Questions
Time And Work QuestionsSquare Root and Cube Root
Number Series QuestionPercentage Aptitude Questions
Problem on HCF and LCMLogarithms Formulas

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