Unitary Method Questions- Detailed Solution

Unitary Method Questions

Some applications of unitary methods:

• Calculating the price of an item when the price of a number of items is given.
• Solving business problems by calculating profit and loss.
• Solving problems related to distance, time and speed.
• Calculating the amount of work and time taken to complete the work.

The questions can be solved by two methods:

• Direct Variation
• Indirect Variation

Solved Examples 

1. Priya went to the market to buy notebooks. The cost of 5 notebooks is Rs 250. Find the price of 3 such notebooks bought by Priya?

Cost of 5 notebooks = Rs 250 (Given)

⇒ Cost of 1 notebook = Rs \frac{250}{5}= Rs 50

∴ Cost of 3 notebooks = Rs (50 × 3) = Rs 150

Hence, the cost of three notebooks bought by Priya is equal to Rs 150.

2. Neha’s father Suresh bought 3 dozen pencils for Rs 360. What is the cost of 7 pencils?

1 dozen = 12

3 dozens = (12 × 3) = 36

Cost of 36 pencils = Rs 360 (Given)

⇒ Cost of 1 pencil =\operatorname{Rs} \frac{360}{36}=\operatorname{Rs} 10

∴ Cost of 7 pencil = Rs (10 × 7) = Rs 70

Hence, the cost of 7 pencils bought by Suresh is equal to Rs 70.

3. Vickey bought 6 apples for Rs 42 and Mohit bought 9 apples for Rs 81. Who bought the apples cheaper?

Cost of 6 apples bought by Vickey = Rs 42

⇒ Cost of 1 apple bought by Vickey =\operatorname{Rs} \frac{42}{6}= Rs 7

Cost of 9 apples bought by Mohit = Rs 81

⇒ Cost of 1 apple bought by Mohit =\operatorname{Rs} \frac{81}{9}= Rs 9

Rs 7 < Rs 9

∴ Cost of 1 apple bought by Vickey < Cost of 1 apple bought by Mohit.

Hence, the apples bought by Vickey were cheaper.

4. The cost of 10 rings is equal to Rs 100. Find the maximum number of rings Sonia can buy if she has Rs 70.

Cost of 10 rings = Rs 100

⇒ Cost of 1 ring =\operatorname{Rs} \frac{100}{10}= Rs 10

Number of rings that can be bought with Rs 10 = 1

⇒ Number of rings that can be bought with Rs 70  =\frac{1}{10} \times 70=7

Hence, Sonia can buy a maximum of 7 rings.

5. 5 packets of Pencil A costs Rs 600 having 10 pencils in each packet. 4 packets of Pencil B costs Rs 500 having 5 pencils in each packet. Which pencil is costlier?

Pencil A
Number of Pencils in 1 packet = 10

Number of Pencils in 5 packets = 10 × 5 = 50

Cost of 50 pencils = Rs 600

Hence, Cost of 1 pencil =\mathrm{Rs} \frac{600}{50}= Rs 12

Pencil B 

Number of pencils in 1 packet = 5

Number of pencils in 4 packets = 5 × 4 = 20

Cost of 20 pencils = Rs 500

Cost of 1 pencil =\operatorname{Rs} \frac{200}{20}= Rs 25

Since, Rs 25 > Rs 12.

∴ Cost of 1 Pencil B > Cost of 1 Pencil A.

Hence, Pencil B is costlier than Pencil A.

6. Pooja can complete building the dollhouse in 6 days and Vickey can complete building the same in 12 days. In how many days the construction of the dollhouse can be completed if they work together?

Fraction of work done by Pooja in 6 days = 1

Fraction of work by Pooja in 1 day =\frac{1}{6}

Fraction of work by Vickey in 12 days = 1

Fraction of work by Vickey in 1 day =\frac{1}{12}

∴  Fraction of work done by Vickey and Pooja together in 1 day =\frac{1}{6}+\frac{1}{8}=\frac{1}{4} 

No. of days taken by both of them to complete \frac{1}{4}of the total work = 1

No. of days taken by both of them to complete the total work =1 \times \frac{4}{1}=4 days

Hence Vickey and Pooja can complete the dollhouse in 4 days if they work together.

7. A motorbike can travel from point A to point B in 2 hours if the speed of the motorbike is 60kmph. Find the time taken by the motorbike to travel the same distance if the speed is 40kmph?

With the decrease in speed, the time taken by the motorbike will increase to travel from point A to point B.

Time taken by the motorbike  when the speed is 60 kmph = 2 hours

Hence, time taken by the motorbike when the speed is 1 kmph = 2 \times 60hours = 120 hours

∴  Time taken by the motorbike when the speed is 40 kmph =120 \div 40= 3 hours

Hence, the time taken by the motorbike when the speed is 40 kmph is equal to 3 hours.

8. Work can be completed by 4 men in 6 days. How many days will be required to complete the work by 3 men?

With the increase in the number of men, the number of days to complete the work will be less.

No. of days taken to complete work by 4 men = 6 days

⇒ No. of days taken to complete the work by 1 man = 6 × 4 days = 24 days 

∴ No. of days taken to complete the work by 3 men =\frac{24}{3}days = 8 days

Hence, 3 men will take 8 days to complete the work.