Gujarat BoardĀ GSEB Textbook Solutions Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.3 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.3

Question 1.

If the cost of 7 m of cloth is ā¹ 294, find the cost of 5 m of cloth.

Solution:

āµ Cost of 7 m of cloth = ā¹ 294

ā“ Cost of 1 m of cloth = \(\frac { ā¹ 294 }{ 7 }\) = ā¹ 42

Cost of 5 m of cloth = ā¹ (42 Ć 5) = ā¹ 210

Thus, the cost of 5 m of cloth ā¹ 210.

Question 2.

Ekta earns ā¹ 1500 in 10 days. How much will she earn in 30 days?

Solution:

Ektaās earning in 10 days = ā¹ 1500

ā“ Ektaās earning in 1 day = \(\frac{ā¹ 1500}{10}\) =ā¹ 150

So Ektaās earning in 30 days = ā¹ (150 Ć 30) = ā¹ 4500

Thus, Ekta will earn ā¹ 4500 in 30 days.

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.

Solution:

āµ Measure of rainfall in 3 days = 276 mm

ā“ Measure of rainfall in 1 day 276

= \(\frac { 276 }{ 3 }\) mm = 92 mm

So, measure of rainfall in 7 days

= (92 Ć 7) mm = 644 mm

Thus, 644 mm of rain will fall in 7 days (in one week).

Question 4.

The cost of 5 kg of wheat is ā¹ 30.50.

(a) What will be the cost of 8 kg of wheat?

(b) What quantity of wheat can be purchased in ā¹ 61?

Solution:

(a)

āµCost of 5 kg of wheat = ā¹ 30.50

ā“Cost of 1 kg of wheat

= ā¹ \(\frac { 30.50 }{ 5 }\) Ć \(\frac { 100 }{ 100 }\) = ā¹ \(\frac { 61 }{ 10 }\)

So, cost of 8 kg of wheat

Thus, the cost of 8 kg of wheat is ā¹ 48.80.

Again, quantity of wheat that can be purchased for \(\frac { 61 }{ 10 }\) = 1 kg

ā“ Quantity of wheat that can be purchased for

ā¹ 1 = \(\frac{1 \times 10}{61}\) kg

So, quantity of wheat that can be purchased for ā¹ 61

\(\frac { 1 Ć 10 }{ 61 }\) Ć 61 kg = 10 kg

10 kg of wheat can be purchased in ā¹ 61

Question 5.

The temperature dropped 15 degrees 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?

Solution:

āµ Drop in temperature in 30 days =15 degree

ā“ Drop in temperature in one day = \(\frac { 15 }{ 30 }\) degree

So, drop in temperature in 10 days

= 10 Ć \(\frac { 15 }{ 30 }\) degrees = 5 degrees

Thus, 5 degree temperature will drop in next 10 days.

Question 6.

Shaina pays ā¹ 7500 as rent for 3 months. How much does she have to pay for a whole year, if the rent per month remains the same?

Solution:

āµ Rent for 3 months = ā¹ 7500

Rent for 1 month = \(\frac { 7500 }{ 3 }\) = ā¹ 2500

ā“ Rent for a whole year (i.e. 12 months)

= ā¹ (12 Ć 2500) = ? 30000

Thus, Shaina will have to pay ā¹ 30,000 for a whole year.

Question 7.

The cost of 4 dozen bananas is ā¹ 60. How many bananas can be purchased for ā¹ 12.50?

Solution:

Since, 1 dozen of bananas = 12 bananas

ā“ 4 dozen of bananas = (12 Ć 4) bananas = 48 bananas

Now, the number of bananas that can be purchased for ā¹ 60 = 48

Number of bananas that can be purchased for ā¹ 1 = \(\frac { 48 }{ 60 }\) = \(\frac{48\div 12}{60 \div 12}\) = \(\frac { 4 }{ 5 }\)

[āµ HCF of 48 and 60 is 12]

ā“ Number of bananas that can be purchased for

ā¹ 12.50 = \(\frac { 4 }{ 5 }\) Ć 12.50 = \(\frac { 4 }{ 5 }\) Ć \(\frac { 1250 }{ 100 }\) = 10

Thus, 10 bananas can be purchased for ā¹ 12.50.

Question 8.

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

Solution:

āµ Weight of 72 books = 9 kg

Weight of 1 book = \(\frac { 9 }{ 72 }\) kg

ā“ Weight of 40 books = 40 Ć \(\frac { 9 }{ 72 }\)kg = 5 kg

Thus, the weight of 40 books is 5 kg.

Question 9.

A truck requires 108 liters 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?

Solution:

āµ Quantity of diesel required for 594 km = 108 litres

Quantity of diesel required for 1 km = \(\frac { 108 }{ 594 }\) litre = \(\left(\frac{108+54}{594+54}\right)\) litres

= \(\frac { 2 }{ 11 }\) litres [āµ HCF of 108 and 594 is 54]

ā“ Quantity of diesel required for 1650 km

= \(\left(\frac{2}{11} \times 60\right)\) litres

= (2 Ć 150) litres = 300 litres.

Thus, 300 liters of diesel will be required to cover 1650 km.

Question 10.

Does Raju purchase 10 pens? 150 and Manish buy 7 pens for ā¹ 84. Can you say who got the pens cheaper?

Solution:

For Raju

āµ Cost of 10 pens = ā¹ 150

ā“ Cost of 1 pen = \(\frac { 150 }{ 10 }\) = ā¹ 15

For Manish

āµ Cost of 7 pens = ā¹ 84

ā“ Cost of 1 pen = \(\frac { 87 }{ 7 }\) = ā¹ 12

Since, ā¹ 12 < ā¹ 15

Thus, Manish got 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?

Solution:

For Anish:

āµ Number of runs made in 6 overs = 42

ā“ Number of runs made in 1 over

= \(\frac { 42 }{ 6 }\) = 7

Thus, Anish made 7 runs per over.

For Anup:

āµ Number of runs made in 7 overs = 63

ā“ Number of runs made in 1 over

= \(\frac { 63 }{ 7 }\) = 9

Thus, Anup made 9 runs per over.

Hence, Anup made more runs per over.