**Question 1.Select the appropriate alternative answer for the following questions.**

**i . If 6 : 5 = y : 20, then what will be the value of y?(A) 15(B) 24(C) 18(D) 22.5Answer:**

(B) 24

**ii. What is the ratio of 1 mm to 1 cm ?(A) 1 : 100(B) 10: 1(C) 1 : 10(D) 100: 1Answer:**

(C) 1 : 10

**iii. The ages of Jatin, Nitin and Mohasin are 16, 24 and 36 years respectively. What is the ratio of Nitin’s age to Mohasin’s age ?(A) 3 : 2(B) 2 : 3(C) 4 : 3(D) 3 : 4Answer:**(B) 2 : 3

**iv. 24 bananas were distributed between Shubham and Anil in the ratio 3 : 5, then how many bananas did Shubham get?(A) 8(B) 15(C) 12(D) 9Answer:**

(D) 9

**v. What is the mean proportional of 4 and 25?(A) 6(B) 8(C) 10(D) 12Answer:**(C) 10

Hints:

iv. 3x + 5x = 24

∴ 8x = 24

∴ x = 3

∴ Number of bananas with Shubham = 3x = 9

v. x^{2} = 4 x 25

∴ x^{2} = 100

∴ x = 10

**Question 2.For the following numbers write the ratio of first number to second number in the reduced form. [1 Mark each]i. 21,48ii. 36,90iii. 65,117iv. 138,161v. 114,133Solution:**

i. 21,48

**Question 3.Write the following ratios in the reduced form.i. Radius to the diameter of a circle.ii. The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm.iii. The ratio of numbers denoting perimeter to area of a square, having side 4 cm.Solution:**

i. Radius to the diameter of a circle.

Let radius of the circle be r

then, diameter = 2 x radius = 2r

Ratio of radius to diameter of circle

∴ Ratio of radius to diameter of circle is 1 : 2.

ii. The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm.

Let □ ABCD be a rectangle.

In ∆ABC, ∠B = 90°

AC^{2} = AB^{2} + BC^{2} … [Pythagoras theorem]

= 4^{2} + 3^{2} = 16 + 9

∴ AC^{2} = 25

AC = 5 … [Taking square root on both side]

= 5 : 4

∴ The ratio of diagonal to the length of a rectangle is 5 : 4

iii. The ratio of numbers denoting perimeter to area of a square, having side 4 cm. side of square = 4cm

Perimeter of square = 4 x side = 4 x 4 = 16 cm

Area of square = (side)^{2} = (4)^{2} = 16 cm^{2}

Ratio of numbers denoting perimeter to area of square

∴ The ratio of numbers denoting perimeter to area of a square is 1 : 1.

**Question 4.Check whether the following numbers are in continued proportion.i. 2, 4, 8ii. 1, 2, 3iii. 9, 12, 16iv. 3, 5, 8Solution:**

If a, b, c are in continued proportion then b

^{2}= ac.

i. 2, 4, 8

Let, a = 2, b = 4 and c = 8

Here, b

^{2}= 4

^{2}= 16

ac = 2 x 8 = 16

∴ b

^{2}= ac

∴ 2, 4,8 are in continued proportion.

ii. 1, 2, 3

Let, a = 1, b = 2 and c = 3

Here, b^{2} = 2^{2} = 4

ac = 1 x 3 = 3

∴ b^{2} ≠ ac

∴ 1, 2,3 are not in continued proportion.

iii. 9, 12, 16

Let, a = 9, b = 12 and c = 16

Here, b^{2} = 12^{2} = 144

ac = 9 x 16 = 144

∴ b^{2} = ac

∴ 9, 12, 16 are in continued proportion.

iv. 3, 5, 8

Let, a = 3, b = 5 and c = 8

Here, b^{2} = 5^{2} = 25

ac = 3 x 8 = 24

∴ b^{2} ≠ ac

∴ 3, 5, 8 are not in continued proportion.

**Question 5.a, b, c are in continued proportion. If a = 3 and c = 27, then find b.Solution:**

a, b, c are in continued proportion. …[Given]

∴ b

^{2}= ac

∴ b

^{2}= 3 x 27 …[∵ a = 3 and c = 27]

∴ b

^{2}= 81

∴ b = 9 …[Taking square root of both sides]

**Question 6.Convert the following ratios into percentages.Solution:**

i. Let 37 : 500 = x%

∴ 37 : 500 = 7.4%

**Question 7.Write the ratio of first quantity to second quantity in the reduced form.i. 1024 MB, 1.2 GB [(1024 MB = 1GB)]ii. ₹ 17, ₹ 25 and 60 paiseiii. 5 dozen, 120 unitsiv. 4 sq.m, 800 sq.cmv. 1.5 kg, 2500 gmSolution:**i. 1024 MB, 1.2 GB

1024 MB = 1 GB

ii. ₹ 17, ₹ 25 and 60 paise

₹ 17 = 17 x 100 paise = 1700 paise

₹ 25 and 60 paise = (25x 100) paise + 60 paise

= (2500 + 60) paise

= 2560 paise

iii. 5 dozen, 120 units

5 dozen = 5 x 12 units = 60 units

iv. 4 sq.m, 800 sq.cm

4 sq.m = 4 x 10000 sq.cm = 40000 sq.cm

v. 1.5 kg, 2500 gm

1.5 kg = 1.5 x 1000 gm = 1500gm

**Question 8.Solution:**

**Question 9.If a, b, c, d are in proportion, then prove thatSolution:**

a, b, c are in continued proportion. …[Given]

**Question 10.If a, b, c are ¡n continued proportion, then prove thatSolution:**

a, b, c are in continued proportion. … [Given]

∴ b = ck

∴ a = bk

= (ck)k . .. [From (j)]

a = ck

^{2}…(ii)

**Question 11.Solve:Solution:**

∴ 29(2x + 3) = 21 (3x + 2)

∴ 5 + 87= 63x + 42

∴ 87 – 42 = 63x – 58x

∴ 45 = 5x

∴ x = 9

∴ x = 9 is the solution of the given equation.

**Question 12.Solution:**

**Question 13.Solution:**

**Question 1.Take 5 pieces of card paper. Write the following statements, one on each paper.Answer:**

i. True

ii. True

iii. False

Here, numerator and denominator are multiplied by two different numbers a and b.

iv. False

Here, different numbers a and b are subtracted from numerator and denominator.

v. True

**Question 2.In the following activity, the values of a and b can be changed. That is by changing a : b we can create many examples. Teachers should give lot of practice to the students and encourage them to construct their own examples. (Textbook pg. no. 70)**

**Question 3.Observe the political map of India from a Geography text book. Study the scale of this map.From the given scale find the straight line distances between various cities like**

i. New Delhi to Bengaluru

ii. Mumbai to Kolkata

iii. Jaipur to Bhuvaneshvar. (Textbook pg. no. 77)

[Students should attempt the above activity on their own.]