Students can practice TS SCERT Class 6 Maths Solutions Chapter 11 Ratio and Proportion Ex 11.3 to get the best methods of solving problems.
TS 6th Class Maths Solutions Chapter 11 Ratio and Proportion Exercise 11.3
Question 1.
A bag of 25 marbles is shared between Rahul and Kiran in the ratio 2:3.
(i) How many marbles does Kiran receive?
(ii) How many marbles does Rahul receive?
Answer:
Ratio of Rahuls marbles to Kiran’s marbles is 2 : 3.
Total parts = 2 + 3 = 5
Total number of marbles = 25
(i) Kirans share of marbles = \(\frac{25 \times 3}{5}\) = 15
(ii) Rahuls share of marbles = \(\frac{25 \times 2}{5}\) = 10
Question 2.
A point X on AB = 14 cm divides it in the ratio 3 : 4. Find the length of AX and XB.
Answer:
Length of line segment AB = 14 cm.
Ratio of line segments \(\overline{\mathrm{AX}}\) and \(\overline{\mathrm{XB}}\) is 3:4
Total parts = 3 + 4 = 7
Length of 7 parts = 14 cm
Length of each part = \(\frac{14}{7}\) = 2 cm
Length of the line segment \(\overline{\mathrm{AX}}\) = 3 × 2 = 6 cm
Length of the line segment \(\overline{\mathrm{XB}}\) = 4 × 2 = 8 cm
Question 3.
Geetha and Laxmi won ₹ 1,050 in a game. They agreed to share the amount in the ratio of 3 : 4. How much does each person receive ?
Answer:
Amount won in the game and shared between Geetha and Laxmi is Rs. 1,050.
Ratio of Geetha’s amount to Laxmi’s amount is 3 : 4.
Total number of parts = 3 + 4 = 7
Value of 7 parts = 1,050
Therefore, value of each part = \(\frac{1050}{7}\) = 150
Geetha’s share = Rs. 150 × 3
Laxmi’s share = Rs. 150 × 4
Question 4.
Divide ₹ 3600 between Satya and Vishnu in the ratio 3:5.
Answer:
Amount that is divided between Satya and Vishnu = ₹ 3,600
Ratio of Satya’s amount to Vishnu’s amount is 3 : 5
Total parts =3 + 5 = 8
Value of 8 parts = ₹ 3,600
Value of each part = ₹ \(\frac{3600}{8}\) = Rs. 450
Satya’s share = ₹ 450 × 3 = ₹ 1350
Vishnu’s share = ₹ 450 × 5 = ₹ 2250
Question 5.
Two numbers are in the ratio 5 : 6. If the sum of the numbers is 132, find the two numbers.
Answer:
Sum of the two numbers = 132
Ratio of two numbers is 5 : 6.
Total parts = 5 + 6 = 11
Value of 11 parts = 132
∴ Value of each part = \(\frac{132}{11}\) = 12
The first number = 12 × 5 = 60
The second number = 12 × 6 = 72
The two numbers are 60 and 72
Question 6.
Estimate the ratio in which X divides AB and then check your estimation by measuring it.
Answer:
The ratio of \(\overline{\mathrm{AX}}\) to \(\overline{\mathrm{XB}}\) is 1 : 1
Verification : \(\overline{\mathrm{AX}}\) = 3.65 ; \(\overline{\mathrm{XB}}\) = 3.65
Question 7.
The income and savings of an employee are in the ratio 11: 2. If his expenditure is ₹ 5346. Then find his income and savings.
Answer:
The ratio of the income and savings of an employee is 11 : 2.
If income is 11 parts, savings 2 parts, then the expenditure will be equal to 9(= 11-2) parts.
Value of 9 parts = ₹ 5346
∴ Value of each part = \(\frac{5346}{9}\) = ₹594
Employee’s income = ₹ 594 × 11 = ₹ 6534
Employee’s savings = ₹ 594 × 2 = ₹ 1188