**Question 1.From the following pairs of numbers, find the reduced form of ratio of first number to second number.i. 72,60ii. 38,57iii. 52,78Solution:**

i. 72, 60

**Question 2.Find the reduced form of the ratio of the first quantity to second quantity.i. ₹ 700, ₹ 308ii. ₹ 14, ₹ 12 and 40 paiseiii. 5 litres, 2500 mliv. 3 years 4 months, 5 years 8 monthsv. 3.8 kg, 1900 gmvi. 7 minutes 20 seconds, 5 minutes 6 secondsSolution:**

i. ₹ 700, ₹ 308

ii. ₹ 14, ₹12 and 40 paise

₹ 14 = 14 x 100 paise = 1400 paise

₹ 12 and 40 paise = 12 x 100 paise + 40 paise

= (1200 + 40) paise

= 1240 paise

iii. 5 litres, 2500 ml

5 litres = 5 x 1000 ml = 5000ml

iv. 3 years 4 months, 5 years 8 months

3 years 4 months = 3×12 months + 4 months

= (36 + 4) months

= 40 months

5 years 8 months = 5 x 12 months + 8 months

= (60 + 8) months

= 68 months

v. 3.8 kg, 1900 gm

3.8 kg = 3.8 x 1000 gm = 3800 gm

vi. 7 minutes 20 seconds, 5 minutes 6 seconds

7 minutes 20 seconds = 7 x 60 seconds + 20 seconds

= (420 + 20) seconds

= 440 seconds

5 minutes 6 seconds = 5 x 60 seconds + 6 seconds

= (300 + 6) seconds

= 306 seconds

**Question 3.Express the following percentages as ratiosi. 75 : 100ii. 44 : 100iii. 6.25%iv. 52: 100v. 0.64%Solution:**

**Question 4.Three persons can build a small house in 8 days. To build the same house in 6 days, how many persons are required?Solution:**

Let the persons required to build a house in 6 days be x.

Days required to build a house and number of persons are in inverse proportion.

∴ 6 × x = 8 × 3

∴ 6 x = 24

∴ x = 4

∴ 4 persons are required to build the house in 6 days.

**Question 5.Convert the following ratios into percentages.i. 15 : 25ii. 47 : 50Solution:**

Let 15 : 25 = x %

∴ 15 : 25 = 60 %

ii. Let 47 : 50 = x%

∴ 47 : 50 = 94 %

**Question 6.The ratio of ages of Abha and her mother is 2 : 5. At the time of Abha’s birth her mothers age was 27 years. Find the present ages of Abha and her mother.Solution:**

The ratio of ages of Abha and her mother is 2 : 5.

Let the common multiple be x.

∴ Present age of Abha = 2x years and

Present age of Abha’s mother = 5x years

According to the given condition, the age of Abha’s mother at the time of Abha’s birth = 27 years

∴ 5x – 2x = 27

∴ 3x = 27

∴ x = 9

∴ Present age of Abha = 2x = 2 x 9 = 18 years

∴ Present age of Abha’s mother = 5x =5 x 9 = 45 years

The present ages of Abha and her mother are 18 years and 45 years respectively.

**Question 7.Present ages of Vatsala and Sara are 14 years and 10 years respectively. After how many years the ratio of their ages will become 5 : 4?Solution:**

Present age of Vatsala = 14 years

Present age of Sara = 10 years

After x years,

Vatsala’s age = (14 + x) years

Sara’s age = (10 + x) years

According to the given condition,

After x years the ratio of their ages will become 5 : 4

∴ 4(14 + x) = 5(10 + x)

∴ 56 + 4x = 50 + 5x

∴ 56 – 50 = 5x – 4x

∴ 6 = x

∴ x = 6

∴ After 6 years, the ratio of their ages will become 5 : 4.

**Question 8.The ratio of present ages of Rehana and her mother is 2 : 7. After 2 years, the ratio of their ages will be 1 : 3. What is Rehana’s present age ?Solution:**

The ratio of present ages of Rehana and her mother is 2 : 7

Let the common multiple be x.

∴ Present age of Rehana = 2x years and Present age of Rehana’s mother = 7x years

After 2 years,

Rehana’s age = (2x + 2) years

Age of Rehana’s mother = (7x + 2) years

According to the given condition,

After 2 years, the ratio of their ages will be 1 : 3

∴ 3(2x + 2) = 1(7x + 2)

∴ 6x + 6 = 7x + 2

∴ 6 – 2 = 7x – 6x

∴ 4 = x

∴ x = 4

∴ Rehana’s present age = 2x = 2 x 4 = 8 years

∴ Rehana’s present age is 8 years.