Chapter 8: Ratio and Proportion

Solution:-

Let us assume the missing number be y.

Then, (3/5) = (y/20)

By cross multiplication, we get,

(3 × 20)/5 = y

y = 60/5

Divide both the numerator and denominator by 5.

y = 12

Therefore, 3/5 = [12]/20

Solution:-

Let us assume the missing number is y.

Then, y/18 = 2/9

By cross multiplication, we get,

y = (2 × 18)/9

y = 36/9

Divide both the numerator and denominator by 9.

y = 4

Therefore, [4]/18 = 2/9

Solution:-

Let us assume the missing number is y.

Then, 8/y = 3.2/4

By cross multiplication, we get,

y = (8 × 4)/3.2

y = 32/3.2

y = 320/32

Divide both the numerator and denominator by 32.

y = 10

Therefore, 8/[10] = 3.2/4

Solution:-

Consider the first two ratios [ ]/45 = 16/40

Let us assume the missing number by P

Then, P/45 = 16/40

By cross multiplication, we get,

P = (16 × 45)/40

P = 720/40

P = 72/4

Divide both the numerator and denominator by 4.

P = 18

Therefore, [18]/45 = 16/40

Now, consider the last two ratios, 16/40 = 24/[ ]

Let us assume the missing number be Q,

Then, 16/40 = 24/Q

By cross multiplication, we get,

Q = (24 × 40)/16

Q = 960/16

Divide both the numerator and denominator by 16.

Q = 60

Therefore, 16/40 = 24/[60]

Solution:-

Consider the first two ratios 16/36 = [ ]/63

Let us assume the missing number is P

Then, 16/36 = P/63

By cross multiplication, we get,

P = (16 × 63)/36

P = 1008/36

Divide both the numerator and denominator by 36.

P = 28

Therefore, 16/36 = [28]/63

Now, consider the middle two ratios, 28/63 = 36/[ ]

Let us assume the missing number is Q,

Then, 28/63 = 36/Q

By cross multiplication, we get,

Q = (36 × 63)/28

Q = 2268/28

Divide both the numerator and denominator by 28.

Q = 81

Therefore, 28/63 = 36/[81]

Consider the last two ratios 36/81 = [ ]/117

Let us assume the missing number is R

Then, 36/81 = R/117

By cross multiplication, we get,

P = (36 × 117)/81

P = 4212/81

Divide both the numerator and denominator by 81.

P = 52

Therefore, 36/81 = [52]/117

So, 16/36 = [28]/63 = 36/[81] = [52]/117

In questions 16 to 34, state whether the given statements are true (T) or false (F).

Solution:-

True.

Consider the two fractions, 3/8 = 15/40

15/40 is further simplified by dividing both the numerator and denominator by 5, and we get,

= 3/8

Therefore, 3/8 = 3/8

Solution:-

True.

Consider the two ratios, 4: 7 = 20: 35

= 4/7 = 20/35

20/35 is further simplified by dividing both the numerator and denominator by 5 we get,

= 4/7

Therefore, 4/7 = 4/7

Solution:-

False.

Consider the two ratios, 0.2: 5 = 2: 0.5

0.2/5 = 2/0.5

0.04 ≠ 4

Solution:-

False.

Consider the two ratios 3: 33 = 33: 333

3/33 = 33/333

0.0909 ≠ 0.0990

Solution:-

False.

Consider the two ratios 15m : 40m = 35m : 65m

15/40 = 35/65

15/40 is further simplified by dividing both the numerator and denominator by 5 we get,

= 3/8

35/65 is further simplified by dividing both the numerator and denominator by 5 we get,

= 7/13

Hence, 3/8 ≠ 7/13

Therefore, 15/40 ≠ 35/65