# Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 3 Ratio and Proportion Ex 3.4

## Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 3 Ratio and Proportion Ex 3.4

Question 1.
Fill in the blanks.
(i) If the cost of 3 pens is ₹ 18, then the cost of 5 pens is ____
(ii) If Karkuzhali earns ₹ 1800 in 15 days, then she earns ₹ 3000 in ___ days
Solution:
(i) ₹ 30
Hint: $$5 \times \frac{18}{3}$$ = 5 × 6 = ₹ 30
(ii) 25 Days
Hint:
$$\frac{1800}{3000}=\frac{15}{x}$$
⇒ x = $$\frac{15 \times 3000}{1800}$$ = 25 days

Question 2.
Say True or False.
(i) If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg.
(ii) A car travels 90 km in 3 hours with constant speed, It will travel 140 km in 5 hours at the same speed.
Solution:
(i) True
Hint: Weight of 1 book = $$\frac{8}{40}=\frac{1}{5} \mathrm{kg}$$
Flence Weight of 15 books = $$\frac{1}{5} \times 15=3 \mathrm{kg}$$
(ii) False
1 hour the car travels = $$\frac{90}{3}$$ = 30 km
In 5 hours the car travels = 30 × 5 = 150 km

Question 3.
If a person reads 20 pages of a book in 2 hours, how many pages will he read in 8 hours at the same speed?
Solution:
Pages read in 2 hours = 20
Then pages read in 1 hour = $$\frac{20}{2}$$ = 10 pages.
Pages will be read in 8 hours = 8 × 10 = 80 pages.
Number of pages will be read in 8 hrs = 80 pages

Question 4.
The cost of 15 chairs is Rs 7500. Find the number of such chairs that can be purchased for Rs 12000?
Solution:Cost of 15 chairs = ₹ 7500
Cost of 1 chair = $$\frac{7500}{15}$$ = 500
For ₹ 500 number of chair purchases = 1
For ₹ 12,000 number of chair purchased = $$\frac{12000}{500}$$ = 24
24 Chairs can be purchased for ₹ 12,000.

Question 5.
A car covers a distance of 125 km in 5 kg of LP Gas. How much distance will it cover in 3 kg of LP Gas?
Solution:
With 5kg LP Gas distance covered = 125 km
With 1 kg LP Gas distance covered = $$\frac{125}{5}$$ = 25 km
With 3 kg LP Gas distance covered = 25 × 3 = 75 km.
75 km can be covered with 3 kg LP Gas.

Question 6.
Cholan walks 6 km in 1 hour at a constant speed. Find the distance covered by him in 20 minutes at the same speed.
Solution:
Distance covered in 1 hour i.e 60 minutes = 6 km
Distance covered in 1 minutes = $$\frac{6}{60}$$ km
Distance covered in 20 minutes = $$\frac{6}{60}$$ × 20 = 2 km
Cholan covers 2 km in 20 minutes.

Question 7.
The number of correct answers given by Kaarmugilan and Kavitha in a quiz competition is in the ratio 10 : 11. If they had scored a total of 84 points in the competition, then how many points did Kavitha get?
Solution:
Correct answers given by Kaarmugilan and Kavitha are in the ratio 10 : 11
Total of 84 points will be divided into 10 + 11 = 21 equal parts
Points scored by Kavitha = $$\frac{11}{21} \times 84$$ = 44 points
Kavitha scored 44 points in the quiz.

Question 8.
Karmegam made 54 runs in 9 overs and Asif made 77 runs in 11 overs. Whose run rate is better? (run rate = ratio of runs to overs)
Solution:
Run rate = Ratio of runs to overs.
Run rate of Karmegam = $$\frac{54}{9}$$ = 6
Run rate of Asif = $$\frac{77}{11}$$ = 7
Asif’s runrate is better.

Question 9.
You purchase 6 apples for ₹ 90 and your Mend purchases 5 apples for ₹ 70. Whose purchase is better?
Solution:
In my purchase cost of 6 apples = ₹ 90
Cost of 1 apple = $$\frac{90}{6}$$ = ₹ 15
In my friend’s purchase cost of 5 apples = ₹ 70
Cost of 1 apple = $$\frac{70}{5}$$ = ₹ 14
My friend buys for a lower price.
My friend’s purchase is a better buy.

Objective Type Questions

Question 10.
If a Barbie doll costs Rs 90, then the cost of 3 such dolls is Rs …….
(a) 260
(b) 270
(c) 30
(d) 93
Solution:
(b) 270

Question 11.
If 8 oranges cost ₹ 56, then the cost of 5 oranges is ₹ _____
(a) 42
(b) 48
(c) 35
(d) 24
Solution:
(c) 35
Hint:
Cost of 1 Orange = $$\frac{56}{8}$$ = ₹ 7
Cost of 5 Orange = 7 × 5 = ₹ 35

Question 12.
If a man walks 2 km in 15 minutes, then he will walk ………. km in 45 minutes.
(a) 10
(b) 8
(c) 6
(d) 12
Solution:
(c) 6