Gujarat Board 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 ₹ 294, find the cost of 5 m of cloth.
Solution:
∵ Cost of 7 m of cloth = ₹ 294
∴ Cost of 1 m of cloth = \(\frac { ₹ 294 }{ 7 }\) = ₹ 42
Cost of 5 m of cloth = ₹ (42 × 5) = ₹ 210
Thus, the cost of 5 m of cloth ₹ 210.
Question 2.
Ekta earns ₹ 1500 in 10 days. How much will she earn in 30 days?
Solution:
Ekta’s earning in 10 days = ₹ 1500
∴ Ekta’s earning in 1 day = \(\frac{₹ 1500}{10}\) =₹ 150
So Ekta’s earning in 30 days = ₹ (150 × 30) = ₹ 4500
Thus, Ekta will earn ₹ 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:
∵ Measure of rainfall in 3 days = 276 mm
∴ Measure of rainfall in 1 day 276
= \(\frac { 276 }{ 3 }\) mm = 92 mm
So, measure of rainfall in 7 days
= (92 × 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 ₹ 30.50.
(a) What will be the cost of 8 kg of wheat?
(b) What quantity of wheat can be purchased in ₹ 61?
Solution:
(a)
∵Cost of 5 kg of wheat = ₹ 30.50
∴Cost of 1 kg of wheat
= ₹ \(\frac { 30.50 }{ 5 }\) × \(\frac { 100 }{ 100 }\) = ₹ \(\frac { 61 }{ 10 }\)
So, cost of 8 kg of wheat
Thus, the cost of 8 kg of wheat is ₹ 48.80.
Again, quantity of wheat that can be purchased for \(\frac { 61 }{ 10 }\) = 1 kg
∴ Quantity of wheat that can be purchased for
₹ 1 = \(\frac{1 \times 10}{61}\) kg
So, quantity of wheat that can be purchased for ₹ 61
\(\frac { 1 × 10 }{ 61 }\) × 61 kg = 10 kg
10 kg of wheat can be purchased in ₹ 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:
∵ Drop in temperature in 30 days =15 degree
∴ Drop in temperature in one day = \(\frac { 15 }{ 30 }\) degree
So, drop in temperature in 10 days
= 10 × \(\frac { 15 }{ 30 }\) degrees = 5 degrees
Thus, 5 degree temperature will drop in next 10 days.
Question 6.
Shaina pays ₹ 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:
∵ Rent for 3 months = ₹ 7500
Rent for 1 month = \(\frac { 7500 }{ 3 }\) = ₹ 2500
∴ Rent for a whole year (i.e. 12 months)
= ₹ (12 × 2500) = ? 30000
Thus, Shaina will have to pay ₹ 30,000 for a whole year.
Question 7.
The cost of 4 dozen bananas is ₹ 60. How many bananas can be purchased for ₹ 12.50?
Solution:
Since, 1 dozen of bananas = 12 bananas
∴ 4 dozen of bananas = (12 × 4) bananas = 48 bananas
Now, the number of bananas that can be purchased for ₹ 60 = 48
Number of bananas that can be purchased for ₹ 1 = \(\frac { 48 }{ 60 }\) = \(\frac{48\div 12}{60 \div 12}\) = \(\frac { 4 }{ 5 }\)
[∵ HCF of 48 and 60 is 12]
∴ Number of bananas that can be purchased for
₹ 12.50 = \(\frac { 4 }{ 5 }\) × 12.50 = \(\frac { 4 }{ 5 }\) × \(\frac { 1250 }{ 100 }\) = 10
Thus, 10 bananas can be purchased for ₹ 12.50.
Question 8.
The weight of 72 books is 9 kg. What is the weight of 40 such books?
Solution:
∵ Weight of 72 books = 9 kg
Weight of 1 book = \(\frac { 9 }{ 72 }\) kg
∴ Weight of 40 books = 40 × \(\frac { 9 }{ 72 }\)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:
∵ 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 [∵ HCF of 108 and 594 is 54]
∴ Quantity of diesel required for 1650 km
= \(\left(\frac{2}{11} \times 60\right)\) litres
= (2 × 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 ₹ 84. Can you say who got the pens cheaper?
Solution:
For Raju
∵ Cost of 10 pens = ₹ 150
∴ Cost of 1 pen = \(\frac { 150 }{ 10 }\) = ₹ 15
For Manish
∵ Cost of 7 pens = ₹ 84
∴ Cost of 1 pen = \(\frac { 87 }{ 7 }\) = ₹ 12
Since, ₹ 12 < ₹ 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:
∵ Number of runs made in 6 overs = 42
∴ Number of runs made in 1 over
= \(\frac { 42 }{ 6 }\) = 7
Thus, Anish made 7 runs per over.
For Anup:
∵ Number of runs made in 7 overs = 63
∴ 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.