Solution:

The ratio of 72 to 60

= \(\displaystyle \frac{72}{60}\)

= \(\displaystyle \frac{6}{5}\)

= 6 ∶ 5

Solution:

The ratio of 38 to 57

= \(\displaystyle \frac{38}{57}\)

= \(\displaystyle \frac{2}{3}\)

= 2 ∶ 3

Solution:

The ratio of 52 to 78

= \(\displaystyle \frac{52}{78}\)

= \(\displaystyle \frac{2}{3}\)

= 2 ∶ 3

Solution:

The ratio of 700 ₹ to 308 ₹

= \(\displaystyle \frac{700 ₹}{308 ₹}\)

= \(\displaystyle \frac{25}{11}\)

= 25 ∶ 11

Solution:

The ratio of 14 ₹ to 12 ₹ 40 paise

= 1400 paise ∶ 1240 paise

= \(\displaystyle \frac{1400 \text{ paise}}{1240 \text{ paise}}\)

= \(\displaystyle \frac{35}{31}\)

= 35 ∶ 31

Solution:

The ratio of 5 litre, 2500 ml

= 5000 ml ∶ 2500 ml

= \(\displaystyle \frac{5000 \text{ ml}}{2500 \text{ ml}}\)

= \(\displaystyle \frac{2}{1}\)

= 2 ∶ 1

Solution:

The ratio of 3 years 4 months, 5 years 8 months

= 48 months ∶ 68 months

= \(\displaystyle \frac{40 \text{ months}}{68 \text{ months}}\)

= \(\displaystyle \frac{10}{17}\)

= 10 ∶ 17

Solution:

The ratio of 3.8 kg, 1900 gm

= 3800 gm ∶ 1900 gm

= \(\displaystyle \frac{3800 \text{ gm}}{1900 \text{ gm}}\)

= \(\displaystyle \frac{2}{1}\)

= 2 ∶ 1

Solution:

The ratio of 7 minutes 20 seconds, 5 minutes 6 seconds

= 440 seconds ∶ 306 seconds

= \(\displaystyle \frac{440 \text{ seconds}}{306 \text{ seconds}}\)

= \(\displaystyle \frac{220}{153}\)

= 220 ∶ 153

Solution:

75 ∶ 100

= \(\displaystyle \frac{75}{100}\)

= \(\displaystyle \frac{3}{4}\)

= 3 ∶ 4

Solution:

44 ∶ 100

= \(\displaystyle \frac{44}{100}\)

= \(\displaystyle \frac{11}{25}\)

= 11 ∶ 25

Solution:

6.25 %

= \(\displaystyle \frac{6.25}{100}\)

= \(\displaystyle \frac{625}{10000}\)

= \(\displaystyle \frac{1}{16}\)

= 1 ∶ 16

Solution:

52 ∶ 100

= \(\displaystyle \frac{52}{100}\)

= \(\displaystyle \frac{13}{25}\)

= 13 ∶ 25

Solution:

0.64 %

= \(\displaystyle \frac{0.64}{100}\)

= \(\displaystyle \frac{64}{10000}\)

= \(\displaystyle \frac{4}{625}\)

= 4 ∶ 625

Solution:

Let, n be the number of persons and d be the number of days required to build the house.

Now, n and d are in inverse proportion.

∴ n × d = k
  (k = constant of variation) ... (i)

When, n = 3, d = 8

 n × d = k
∴ 3 × 8 = k
∴ 24 = k
i.e. k = 24... (ii)

∴ n × d = 24
  (Equation of variation) ... (iii)

Now, when d = 6, n = ?

When, n = 3, d = 8

 n × 6 = 24

∴ \(\displaystyle n = \frac{24}{6}\)

∴ \(\displaystyle n = 4\) ... (iv)

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

Solution:

15 ∶ 25

= \(\displaystyle \frac{15}{25}\)

= \(\displaystyle \frac{15 \times 4}{25 \times 4}\)

= \(\displaystyle \frac{60}{100}\)

= 60 %

Solution:

47 ∶ 50

= \(\displaystyle \frac{47}{50}\)

= \(\displaystyle \frac{47 \times 2}{50 \times 2}\)

= \(\displaystyle \frac{94}{100}\)

= 94 %

Solution:

7 ∶ 10

= \(\displaystyle \frac{7}{10}\)

= \(\displaystyle \frac{7 \times 10}{10 \times 10}\)

= \(\displaystyle \frac{70}{100}\)

= 70 %

Solution:

546 ∶ 600

= \(\displaystyle \frac{546}{600}\)

= \(\displaystyle \frac{546 \div 100}{600 \div 100}\)

= \(\displaystyle \frac{91}{100}\)

= 91 %

Solution:

7 ∶ 16

= \(\displaystyle \frac{7}{16}\)

= \(\displaystyle \frac{7 \times \displaystyle {\frac {100}{16}}}{16 \times \displaystyle {\frac {100}{16}}}\)

= \(\displaystyle \frac{\displaystyle {\frac {700}{16}}}{100}\)

= \(\displaystyle \frac{43.75}{100}\)

= 43.75 %

Solution:

The ratio of ages of Abha and her mother is 2 ∶ 5.
∴ Let Abha’s age be 2x years and her mother’s age be 5x years.
Now, at the time of Abha’s birth her mother’s age was 27 years.
∴ 5x − 2x = 27
∴ 3x = 27

∴ \(\displaystyle x = \frac{27}{3}\)

∴ \(\displaystyle x = 9\) ... (i)

∴ Abha’s age
= 2x
= 2 × 9
= 18 years

And her mother’s age
= 5x
= 5 × 9
= 45 years

∴ Abha’s age is 18 years and her mother’s age is 45 years.

Solution:

Let that number be x.

∴ \(\displaystyle \frac{14 + x}{10 + x} = \frac{5}{4}\)

∴ 4(14 + x) = 5(10 + x)
∴ 56 + 4x = 50 + 5x
∴ 4x − 5x = 50 − 56
∴ − x = − 6
i.e. x = 6 ... (i)
∴ After 6 years, the ratio of their ages will become 5 ∶ 4.

Solution:

The ratio of present ages of Rehana and her mother is 2 ∶ 7.
∴ Let Rehana’s present age be 2x years and her mother’s present age be 7x years.

After two years,
Rehana’s age = 2x + 2 years
And her mother’s age = 7x + 2 years

From the given information,

  \(\displaystyle \frac{2x + 2}{7x + 2} = \frac{1}{3}\)

∴ 3(2x + 2) = 1(7x + 2)
∴ 6x + 6 = 7x + 2
∴ 6x − 7x = 2 − 6
∴ − x = − 4
i.e. x = 4 ... (i)

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

∴ Rehana’s present age is 8 years.