NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.3

NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.3 UNITARY METHOD

Find here step by step NCERT Solutions for Class 6 Maths Exercise 12.3 Chapter 12 Ratio And Proportion. NCERT Solutions for Class 6 Maths Exercise 12.3 deals with a concept of problem solving called Unitary method.

Prerequisite / Revise this :

Unitary Method : The method in which we first find the value of one unit and then the value of the required number of units is known as the unitary method.

• Suppose the cost of 5 bottles cans is ₹ 150. To find the cost of 3 bottles, using the unitary method, we first find the cost of 1 bottle. It is ₹ 150/5 or ₹ 30. From this, we find the price of 3 bottles as ₹ 30 × 3 or ₹ 90.

EXERCISE 12.3

QUESTION 1

If the cost of 7 m of cloth is ₹ 294, find the cost of 5 m of cloth.

ANSWER

Cost of 7 m of cloth = ₹ 294,

So, cost of 1 m of cloth = ₹ \frac{294}{7} = ₹ 42

Therefore, cost of 5 m of cloth = ₹ 42 × 5 = ₹ 210.

QUESTION 2

Ekta earns ₹ 1500 in 10 days. How much will she earn in 30 days?

ANSWER

Ekta earns in 10 days = ₹ 1500

So, Ekta earns in 1 days = ₹ \frac{1500}{10} = ₹ 150

So, Ekta will earn in 30 days = ₹ 150 × 30 = ₹ 4500

QUESTION 3

If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.

ANSWER

Rainfall in last 3 days = 276 mm,

So, rainfall in 1 day = \frac{276}{3} mm = 92 mm,

Therefore, rainfall in one full week = 92 × 7 mm
= 644 mm = 64.4 cm

Thus, 64.4 cm of rain will fall in one full week (7 days) if the rain continues to fall at the same rate.

QUESTION 4

Cost of 5 kg of wheat is ₹ 30.50.
(a) What will be the cost of 8 kg of wheat?
(b) What quantity of wheat can be purchased in ₹ 61?

ANSWER

Cost of 5 kg of wheat = ₹ 30.50
(a) Cost of 1 kg of wheat = ₹ \frac{30.50}{5} = ₹ 6.10

Therefore, cost of 8 kg of wheat = ₹ 6.10 × 8 = ₹ 48.80,

(b) Quantity of wheat that can be purchased in ₹ 30.50 = 5 kg,

So, quantity of wheat that can be purchased in ₹ 1 = \frac{5}{30.50}

Therefore, quantity of wheat that can be purchased in ₹ 61 = \frac{5}{30.50}\times 61 kg
= 5×2 kg = 10 kg

QUESTION 5

The temperature dropped 15 degree celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?

ANSWER

Drop in temperature in last 30 days = 15° C

The rate of temperature drop remains same,

So, drop in temperature in 1 day = \frac{15}{30} °C = \frac{1}{2} °C,

Therefore, temperature drop in next ten days = \frac{1}{2}\times 10 °C = 5 °C.

QUESTION 6

Shaina pays ₹ 7500 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?

ANSWER

Amount Shain paid as rent for 3 months = ₹ 7500,

So, amount she paid as rent for 1 month = ₹ \frac{7500}{3}
= ₹ 2500,

The rent per month remains same,

Therefore, amount she has to pay for a whole year = ₹ 2500 × 12
= ₹ 30,000.

QUESTION 7

Cost of 4 dozens bananas is ₹ 60. How many bananas can be purchased for
₹ 12.50?

ANSWER

Number of bananas that can be purchased for ₹ 60 = 4 dozens
= 4 × 12 = 48,

So, number of bananas that can be purchased for ₹ 1 = \frac{48}{60}
= \frac{4}{5}

Therefore, number of bananas that can be purchased for ₹ 12.50 = \frac{4}{5}\times 12.50
= 4 × 2.50 = 10.

QUESTION 8

The weight of 72 books is 9 kg. What is the weight of 40 such books?

ANSWER

Weight of 72 books = 9 kg,

So, weight of 1 such book = \frac{9}{72}
= \frac{1}{8}

Therefore, weight of 40 such books = \frac{1}{8}\times 40 kg
= 5 kg

QUESTION 9

A truck requires 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?

ANSWER

Amount of diesel required by the truck to cover 594 km = 108 litres,

So, amount of diesel required by the truck to cover 1 km = \frac{108}{594} litres
= \frac{2}{11} litres,

Therefore, amount of diesel required by the truck to cover 1650 km = \frac{2}{11}\times 1650 litres
= 2 × 150 litres = 300 litres.

QUESTION 10

Raju purchases 10 pens for ₹ 150 and Manish buys 7 pens for ₹ 84. Can you say who got the pens cheaper?

ANSWER

Cost of 10 pens purchased by Raju = ₹ 150,

So, cost of 1 pen purchased by Raju = ₹ \frac{150}{10} = ₹ 10,

Cost of 7 pens purchased by Manish = ₹ 84,

So, cost of 1 pen purchased by Manish = ₹ \frac{84}{7} = ₹ 12,

Since, cost per pen of Raju is less than cost per pen of Manish, therefore Raju got the pens cheaper.

QUESTION 11

Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?

ANSWER

Runs made by Anish in 6 overs = 42 runs,

So, runs made by Anish in 1 over (or per over) = \frac{42}{6} = 7 runs,

Runs made by Anup in 7 overs = 63 runs,

So, runs made by Anup in 1 over (or per over) = \frac{63}{7} = 9 runs,

Since, runs scored by Anup per over is more tha Anish, therefore Anup made more runs per over.

NCERT SOLUTIONS FOR CLASS 6 MATHS CHAPTER 12 RATIO AND PROPORTION

Check NCERT Solutions of other exercises from Class 6 Maths Chapter 12 Ratio and Proportion by clicking the links given below.

Exercise 12.1
Exercise 12.2
Exercise 12.3

We hope Ncert Solutions for Class 6 Maths Exercise 12.3 has helped you understand how to apply Unitary method in problem solving.

Write in the comment section for any error or any solution related queries from the exercise. [ Ncert Solutions for Class 6 Maths Exercise 12.3 ]

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