Percentage and its Applications — Exercise 7.1

Express the following percentage as fraction:

356%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to simplest form.

$\Rightarrow 356 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{356}{100}\\[1em] \Rightarrow \dfrac{89}{25}\\[1em] \Rightarrow 3\dfrac{14}{25}$

Hence, 356% = $\mathbf{3\dfrac{14}{25}}$.

Express the following percentage as fraction:

$2\dfrac{1}{2}$%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to simplest form.

$2\dfrac{1}{2}$% = $\dfrac{5}{2}$%

$\Rightarrow \dfrac{5}{2} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{5}{200}\\[1em] \Rightarrow \dfrac{1}{40}$

Hence, $\mathbf{2\dfrac{1}{2}}$% = $\mathbf{\dfrac{1}{40}}$.

Express the following percentage as fraction:

$16\dfrac{2}{3}$%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to simplest form.

$16\dfrac{2}{3}$% = $\dfrac{50}{3}$%

$\Rightarrow \dfrac{50}{3} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{50}{300}\\[1em] \Rightarrow \dfrac{1}{6}$

Hence, $\mathbf{16\dfrac{2}{3}}$% = $\mathbf{\dfrac{1}{6}}$.

Express the following fraction as percentage:

$\dfrac{3}{2}$

Answer

To convert a fraction into a percentage, multiply the fraction by 100 and put the % sign.

$\Rightarrow \dfrac{3}{2} \times 100$%

$\Rightarrow \dfrac{300}{2}$%

⇒ 150%

Hence, $\mathbf{\dfrac{3}{2}}$ = 150%.

Express the following fraction as percentage:

$\dfrac{9}{20}$

Answer

To convert a fraction into a percentage, multiply the fraction by 100 and put the % sign.

$\Rightarrow \dfrac{9}{20} \times 100$%

$\Rightarrow \dfrac{900}{20}$%

⇒ 45%

Hence, $\mathbf{\dfrac{9}{20}}$ = 45%.

Express the following fraction as percentage:

$1\dfrac{1}{4}$

Answer

To convert a fraction into a percentage, multiply the fraction by 100 and put the % sign.

$1\dfrac{1}{4}$ = $\dfrac{5}{4}$

$\Rightarrow \dfrac{5}{4} \times 100$%

$\Rightarrow \dfrac{500}{4}$%

⇒ 125%

Hence, $\mathbf{1\dfrac{1}{4}}$ = 125%.

Express the following fraction as decimal. Then express the decimal as percentage:

$\dfrac{3}{4}$

Answer

$\dfrac{3}{4}$ = 0.75

To convert a decimal into a percentage, multiply the decimal by 100 and put the % sign.

⇒ 0.75 = (0.75 x 100)% = 75%

Hence, $\mathbf{\dfrac{3}{4}}$ = 0.75 = 75%.

Express the following fraction as decimal. Then express the decimal as percentage:

$\dfrac{5}{8}$

Answer

$\dfrac{5}{8}$ = 0.625

To convert a decimal into a percentage, multiply the decimal by 100 and put the % sign.

⇒ 0.625 = (0.625 x 100)% = 62.5%

Hence, $\mathbf{\dfrac{5}{8}}$ = 0.625 = 62.5%.

Express the following fraction as decimal. Then express the decimal as percentage:

$\dfrac{3}{16}$

Answer

$\dfrac{3}{16}$ = 0.1875

To convert a decimal into a percentage, multiply the decimal by 100 and put the % sign.

⇒ 0.1875 = (0.1875 x 100)% = 18.75%

Hence, $\mathbf{\dfrac{3}{16}}$ = 0.1875 = 18.75%.

Express the following fraction as decimal correct to four decimal places. Then express the decimal as percentage:

$\dfrac{2}{3}$

Answer

$\dfrac{2}{3}$ = 0.66666.....

Correct to four decimal places,

$\dfrac{2}{3}$ = 0.6667

To convert a decimal into a percentage, multiply the decimal by 100 and put the % sign.

⇒ 0.6667 = (0.6667 x 100)% = 66.67%

Hence, $\mathbf{\dfrac{2}{3}}$ = 0.6667 = 66.67%.

Express the following fraction as decimal correct to four decimal places. Then express the decimal as percentage:

$\dfrac{5}{6}$

Answer

$\dfrac{5}{6}$ = 0.83333.....

Correct to four decimal places,

$\dfrac{5}{6}$ = 0.8333

To convert a decimal into a percentage, multiply the decimal by 100 and put the % sign.

⇒ 0.8333 = (0.8333 x 100)% = 83.33%

Hence, $\mathbf{\dfrac{5}{6}}$ = 0.8333 = 83.33%.

Express the following fraction as decimal correct to four decimal places. Then express the decimal as percentage:

$\dfrac{4}{7}$

Answer

$\dfrac{4}{7}$ = 0.571428.....

Correct to four decimal places,

$\dfrac{4}{7}$ = 0.5714

To convert a decimal into a percentage, multiply the decimal by 100 and put the % sign.

⇒ 0.5714 = (0.5714 x 100)% = 57.14%

Hence, $\mathbf{\dfrac{4}{7}}$ = 0.5714 = 57.14%.

Express the following ratio as percentage:

17 : 20

Answer

To convert a ratio into a percentage, first convert the given ratio into a fraction and then convert the fraction into a percentage.

⇒ 17 : 20

$\Rightarrow \dfrac{17}{20}$

$\Rightarrow \dfrac{17}{20} \times 100$%

$\Rightarrow \dfrac{1700}{20}$%

⇒ 85%

Hence, 17 : 20 = 85%.

Express the following ratio as percentage:

13 : 18

Answer

To convert a ratio into a percentage, first convert the given ratio into a fraction and then convert the fraction into a percentage.

⇒ 13 : 18

$\Rightarrow \dfrac{13}{18}$

$\Rightarrow \dfrac{13}{18} \times 100$%

$\Rightarrow \dfrac{1300}{18}$%

$\Rightarrow \dfrac{650}{9}$%

$\Rightarrow 72\dfrac{2}{9}$%

Hence, 13 : 18 = $\mathbf{72\dfrac{2}{9}}$%.

Express the following ratio as percentage:

93 : 80

Answer

To convert a ratio into a percentage, first convert the given ratio into a fraction and then convert the fraction into a percentage.

⇒ 93 : 80

$\Rightarrow \dfrac{93}{80}$

$\Rightarrow \dfrac{93}{80} \times 100$%

$\Rightarrow \dfrac{9300}{80}$%

⇒ 116.25%

Hence, 93 : 80 = 116.25%.

Express the following percentage as decimal:

20%

Answer

To convert a percentage into a decimal, first convert the percentage into a fraction by replacing the % sign with $\dfrac{1}{100}$, then convert the fraction into a decimal.

$\Rightarrow \dfrac{20}{100}$

⇒ 0.2

Hence, 20% = 0.2.

Express the following percentage as decimal:

2%

Answer

To convert a percentage into a decimal, first convert the percentage into a fraction by replacing the % sign with $\dfrac{1}{100}$, then convert the fraction into a decimal.

$\Rightarrow \dfrac{2}{100}$

⇒ 0.02

Hence, 2% = 0.02.

Express the following percentage as decimal:

$3\dfrac{1}{4}$%

Answer

To convert a percentage into a decimal, first convert the percentage into a fraction by replacing the % sign with $\dfrac{1}{100}$, then convert the fraction into a decimal.

$3\dfrac{1}{4}$% = $\dfrac{13}{4}$%

$\Rightarrow \dfrac{13}{4} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{13}{400}\\[1em] \Rightarrow 0.0325$

Hence, $\mathbf{3\dfrac{1}{4}}$% = 0.0325.

Find the value of:

27% of ₹50

Answer

To find a percentage of a given quantity, change the percentage into a fraction and multiply it by the given quantity.

$\Rightarrow \dfrac{27}{100} \times 50\\[1em] \Rightarrow \dfrac{1350}{100}\\[1em] \Rightarrow ₹13.50$

Hence, 27% of ₹50 = ₹13.50.

Find the value of:

$6\dfrac{1}{4}$% of 25 kg

Answer

To find a percentage of a given quantity, change the percentage into a fraction and multiply it by the given quantity.

$6\dfrac{1}{4}$% of 25 kg = $\dfrac{25}{4}$% of 25 kg

$\Rightarrow \dfrac{25}{4} \times \dfrac{1}{100} \times 25\\[1em] \Rightarrow \dfrac{625}{400}\\[1em] \Rightarrow \dfrac{25}{16}\\[1em] \Rightarrow 1\dfrac{9}{16} \text{ kg}$

Hence, $\mathbf{6\dfrac{1}{4}}$% of 25 kg = $\mathbf{1\dfrac{9}{16}}$ kg.

What percent is:

300 g of 2 kg

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

2 kg = (2 x 1000) g = 2000 g

Required percentage = $\dfrac{300}{2000} \times 100$%

= $\dfrac{30000}{2000}$%

= 15%

Hence, 300 g is 15% of 2 kg.

What percent is:

₹7.50 of ₹6

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

Required percentage = $\dfrac{7.50}{6} \times 100$%

= $\dfrac{750}{6}$%

= 125%

Hence, ₹7.50 is 125% of ₹6.

What percent of:

50 kg is 65 kg

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

Required percentage = $\dfrac{65}{50} \times 100$%

= $\dfrac{6500}{50}$%

= 130%

Hence, 65 kg is 130% of 50 kg.

What percent of:

₹9 is ₹4?

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

Required percentage = $\dfrac{4}{9} \times 100$%

= $\dfrac{400}{9}$%

= $44\dfrac{4}{9}$%

Hence, ₹4 is $\mathbf{44\dfrac{4}{9}}$% of ₹9.

If $16\dfrac{2}{3}$% of a number is 25, find the number.

Answer

Let the required number be $x$.

$16\dfrac{2}{3}$% = $\dfrac{50}{3}$%

According to the given condition,

$\dfrac{50}{3}$% of $x$ = 25

$\Rightarrow \dfrac{50}{3} \times \dfrac{1}{100} \times x = 25 \\[1em] \Rightarrow \dfrac{50x}{300} = 25 \\[1em] \Rightarrow \dfrac{x}{6} = 25 \\[1em] \Rightarrow x = 25 \times 6 \\[1em] \Rightarrow x = 150$

Hence, the required number is 150.

If 13.25% of a number is 159, find the number.

Answer

Let the required number be $x$.

According to the given condition,

13.25% of $x$ = 159

$\Rightarrow \dfrac{13.25}{100} \times x = 159 \\[1em] \Rightarrow \dfrac{13.25x}{100} = 159 \\[1em] \Rightarrow x = \dfrac{159 \times 100}{13.25} \\[1em] \Rightarrow x = \dfrac{15900}{13.25} \\[1em] \Rightarrow x = 1200$

Hence, the required number is 1200.

Increase the number 60 by 30%

Answer

If we increase the number 60 by 30%, we get

$\text{New number} = 60 + 60 \times \dfrac{30}{100} \\[1em] = \Big(1 + \dfrac{30}{100}\Big) \times 60 \\[1em] = \dfrac{130}{100} \times 60 \\[1em] = \dfrac{13}{10} \times 60 \\[1em] = \dfrac{780}{10}\\[1em] = 78$

Hence, on increasing 60 by 30% we get 78.

Decrease the number 750 by 10%

Answer

If we decrease the number 750 by 10%, we get

$\text{New number} = 750 - 750 \times \dfrac{10}{100} \\[1em] = \Big(1 - \dfrac{10}{100}\Big) \times 750 \\[1em] = \dfrac{90}{100} \times 750 \\[1em] = \dfrac{9}{10} \times 750 \\[1em] = \dfrac{6750}{10}\\[1em] = 675$

Hence, on decreasing 750 by 10% we get 675.

What number when increased by 15% becomes 299?

Answer

Let the required number be $x$.

Since the number is increased by 15%, we get

$\text{New number} = \Big(1 + \dfrac{15}{100}\Big) \times x \\[1em] \Rightarrow 299 = \dfrac{115}{100} \times x \\[1em] \Rightarrow x = \dfrac{299 \times 100}{115} \\[1em] \Rightarrow x = \dfrac{29900}{115} \\[1em] \Rightarrow x = 260$

Hence, the required number is 260.

On decreasing a number by 18%, it becomes 697. Find the number.

Answer

Let the required number be $x$.

Since the number is decreased by 18%, we get

$\text{New number} = \Big(1 - \dfrac{18}{100}\Big) \times x \\[1em] \Rightarrow 697 = \dfrac{82}{100} \times x \\[1em] \Rightarrow x = \dfrac{697 \times 100}{82} \\[1em] \Rightarrow x = \dfrac{69700}{82} \\[1em] \Rightarrow x = 850$

Hence, the required number is 850.

Mr. Khanna spent 83% of his salary and saved ₹9,350. Calculate his monthly salary.

Answer

Given:

Percentage of salary spent = 83%

Savings = ₹9,350

Percentage of salary saved = (100 - 83)% = 17%

Let the monthly salary of Mr. Khanna be ₹$x$.

According to the given condition,

17% of $x$ = 9350

$\Rightarrow \dfrac{17}{100} \times x = 9350 \\[1em] \Rightarrow \dfrac{17x}{100} = 9350 \\[1em] \Rightarrow x = \dfrac{9350 \times 100}{17} \\[1em] \Rightarrow x = \dfrac{935000}{17} \\[1em] \Rightarrow x = 55000$

Hence, the monthly salary of Mr. Khanna is ₹55,000.

In a school, 38% of the students are girls. If the number of boys is 1023, find the total strength of the school.

Answer

Given:

Percentage of girls in the school = 38%

Number of boys = 1023

Percentage of boys in the school = (100 - 38)% = 62%

Let the total strength of the school be $x$.

According to the given condition,

62% of $x$ = 1023

$\Rightarrow \dfrac{62}{100} \times x = 1023 \\[1em] \Rightarrow \dfrac{62x}{100} = 1023 \\[1em] \Rightarrow x = \dfrac{1023 \times 100}{62} \\[1em] \Rightarrow x = \dfrac{102300}{62} \\[1em] \Rightarrow x = 1650$

Hence, the total strength of the school is 1650.

The price of an article increases from ₹960 to ₹1,080. Find the percentage increase in the price.

Answer

Given:

Original price of the article = ₹960

New price of the article = ₹1,080

Increase in price = New price - Original price

= ₹1,080 - ₹960

= ₹120

Percentage increase = $\dfrac{\text{Increase in price}}{\text{Original price}} \times 100$%

= $\dfrac{120}{960} \times 100$%

= $\dfrac{12000}{960}$%

= 12.5%

Hence, the percentage increase in the price is 12.5%.

In a straight contest, the loser polled 42% votes and lost by 14400 votes. Find the total number of votes polled. If the total number of eligible voters was 1 lakh, find what percentage of voters did not vote.

Answer

Given:

Percentage of votes polled by the loser = 42%

The loser lost by 14400 votes.

There are only two candidates in a straight contest.

Since the loser got 42% votes, therefore, the winner got (100 - 42)% votes = 58% votes

Difference in percentage of votes = (58 - 42)% = 16%

As the loser lost by 14400 votes, so difference in votes = 14400

∴ 16% of total votes polled = 14400

Let the total votes polled be $x$.

$\Rightarrow \dfrac{16}{100} \times x = 14400 \\[1em] \Rightarrow \dfrac{16x}{100} = 14400 \\[1em] \Rightarrow x = \dfrac{14400 \times 100}{16} \\[1em] \Rightarrow x = \dfrac{1440000}{16} \\[1em] \Rightarrow x = 90000$

∴ Total number of votes polled = 90000

Total number of eligible voters = 1 lakh = 100000

Number of voters who did not vote = 100000 - 90000 = 10000

Percentage of voters who did not vote = $\dfrac{10000}{100000} \times 100$%

= $\dfrac{1000000}{100000}$%

= 10%

Hence, the total number of votes polled is 90000 and 10% of the voters did not vote.

Out of 8000 candidates, 60% were boys. If 80% of the boys and 90% of the girls passed the exam, find the number of candidates who failed.

Answer

Given:

Total number of candidates = 8000

Percentage of boys = 60%

Number of boys = 60% of 8000

$= \dfrac{60}{100} \times 8000 \\[1em] = \dfrac{480000}{100} \\[1em] = 4800$

Number of girls = 8000 - 4800 = 3200

Number of boys who passed = 80% of 4800

$= \dfrac{80}{100} \times 4800 \\[1em] = \dfrac{384000}{100} \\[1em] = 3840$

Number of girls who passed = 90% of 3200

$= \dfrac{90}{100} \times 3200 \\[1em] = \dfrac{288000}{100} \\[1em] = 2880$

Total number of candidates who passed = 3840 + 2880 = 6720

Number of candidates who failed = Total candidates - Candidates who passed

= 8000 - 6720

= 1280

Hence, the number of candidates who failed is 1280.

On increasing the price of an article by 16%, it becomes ₹1,479. What was its original price?

Answer

Given:

New price of the article = ₹1,479

Increase in price = 16%

Let the original price of the article be ₹$x$.

Since the price has been increased by 16%, we get

$\text{New price} = \Big(1 + \dfrac{16}{100}\Big) \text{ of original price} \\[1em] \Rightarrow 1479 = \dfrac{116}{100} \times x \\[1em] \Rightarrow x = \dfrac{1479 \times 100}{116} \\[1em] \Rightarrow x = \dfrac{147900}{116} \\[1em] \Rightarrow x = 1275$

Hence, the original price of the article is ₹1,275.

Prachi reduced her weight by 15%. If now she weighs 59.5 kg, what was her earlier weight?

Answer

Given:

Present weight of Prachi = 59.5 kg

Reduction in weight = 15%

Let the earlier weight of Prachi be $x$ kg.

Since the weight has been reduced by 15%, we get

$\text{Present weight} = \Big(1 - \dfrac{15}{100}\Big) \text{ of earlier weight} \\[1em] \Rightarrow 59.5 = \dfrac{85}{100} \times x \\[1em] \Rightarrow x = \dfrac{59.5 \times 100}{85} \\[1em] \Rightarrow x = \dfrac{5950}{85} \\[1em] \Rightarrow x = 70$

Hence, the earlier weight of Prachi was 70 kg.

In a sale, a shop reduces all its prices by 15%. Calculate:

(i) the cost of an article which was originally priced at ₹40

(ii) the original price of an article which was sold for ₹20.40

Answer

Given:

Reduction in all the prices = 15%

(i) Original price of the article = ₹40

$\text{Cost of the article in the sale} = \Big(1 - \dfrac{15}{100}\Big) \times 40 \\[1em] = \dfrac{85}{100} \times 40 \\[1em] = \dfrac{3400}{100} \\[1em] = ₹34$

Hence, the cost of the article in the sale is ₹34.

(ii) Sale price of the article = ₹20.40

Let the original price of the article be ₹$x$.

Since the price has been reduced by 15%, we get

$\text{Sale price} = \Big(1 - \dfrac{15}{100}\Big) \text{ of original price} \\[1em] \Rightarrow 20.40 = \dfrac{85}{100} \times x \\[1em] \Rightarrow x = \dfrac{20.40 \times 100}{85} \\[1em] \Rightarrow x = \dfrac{2040}{85} \\[1em] \Rightarrow x = 24$

Hence, the original price of the article is ₹24.

Increase a price of ₹200 by 10% and then decrease the new price by 10%. Is the final price same as the original one?

Answer

Given:

Original price = ₹200

Increasing the price of ₹200 by 10%,

$\text{New price} = \Big(1 + \dfrac{10}{100}\Big) \times 200 \\[1em] = \dfrac{110}{100} \times 200 \\[1em] = \dfrac{22000}{100} \\[1em] = ₹220$

Now decreasing the new price of ₹220 by 10%,

$\text{Final price} = \Big(1 - \dfrac{10}{100}\Big) \times 220 \\[1em] = \dfrac{90}{100} \times 220 \\[1em] = \dfrac{19800}{100} \\[1em] = ₹198$

Original price = ₹200 and final price = ₹198.

As ₹198 < ₹200, the final price is not the same as the original price.

Hence, the final price ₹198 is not the same as the original price ₹200.

A candidate who gets 36% marks in an examination fails by 24 marks but another candidate, who gets 43% marks, gets 18 more marks than the minimum pass marks. Find the maximum marks and the percentage of pass marks.

Answer

Given:

First candidate gets 36% marks and fails by 24 marks.

Second candidate gets 43% marks and gets 18 marks more than the pass marks.

Let the maximum marks be $x$.

In the first case,

Passing marks = 36% of $x$ + 24

$= \dfrac{36}{100} \times x + 24$

In the second case,

Passing marks = 43% of $x$ - 18

$= \dfrac{43}{100} \times x - 18$

Since pass marks are same in both the cases,

$\Rightarrow \dfrac{43}{100} \times x - 18 = \dfrac{36}{100} \times x + 24 \\[1em] \Rightarrow \dfrac{43x}{100} - \dfrac{36x}{100} = 24 + 18 \\[1em] \Rightarrow \dfrac{7x}{100} = 42 \\[1em] \Rightarrow x = \dfrac{42 \times 100}{7} \\[1em] \Rightarrow x = \dfrac{4200}{7} \\[1em] \Rightarrow x = 600$

∴ Maximum marks = 600

Passing marks = 36% of 600 + 24

$= \dfrac{36}{100} \times 600 + 24 \\[1em] = \dfrac{21600}{100} + 24 \\[1em] = 216 + 24 \\[1em] = 240$

Percentage of passing marks = $\dfrac{240}{600} \times 100$%

= $\dfrac{24000}{600}$%

= 40%

Hence, the maximum marks are 600 and the percentage of passing marks is 40%.

The sides of a rectangle are 20 cm and 15 cm. If each side is increased by 20%, find the percentage increase in the area.

Answer

Given:

Length of the rectangle = 20 cm

Breadth of the rectangle = 15 cm

Original area of the rectangle = Length x Breadth

= 20 x 15

= 300 cm²

Each side is increased by 20%.

$\text{New length} = \Big(1 + \dfrac{20}{100}\Big) \times 20 \\[1em] = \dfrac{120}{100} \times 20 \\[1em] = \dfrac{2400}{100} \\[1em] = 24 \text{ cm}\\[1em] \text{New breadth} = \Big(1 + \dfrac{20}{100}\Big) \times 15 \\[1em] = \dfrac{120}{100} \times 15 \\[1em] = \dfrac{1800}{100} \\[1em] = 18 \text{ cm}$

New area of the rectangle = 24 x 18 = 432 cm²

Increase in area = New area - Original area

= 432 - 300

= 132 cm²

Percentage increase in area = $\dfrac{\text{Increase in area}}{\text{Original area}} \times 100$%

= $\dfrac{132}{300} \times 100$%

= $\dfrac{13200}{300}$%

= 44%

Hence, the percentage increase in the area is 44%.

Imran gives 1% of his monthly income to his two sons as pocket money. The elder son gets 80% of the total amount given and he spends 80% of his share. If he saves ₹60 per month, determine Imran's monthly income.

Answer

Given:

Pocket money given to the two sons = 1% of monthly income

Share of the elder son = 80% of the pocket money

Amount spent by the elder son = 80% of his share

Savings of the elder son = ₹60

Let Imran's monthly income be ₹$x$.

Total pocket money given = 1% of $x$

$= \dfrac{1}{100} \times x \\[1em] = \dfrac{x}{100}$

Share of the elder son = 80% of $\dfrac{x}{100}$

$= \dfrac{80}{100} \times \dfrac{x}{100} \\[1em] = \dfrac{80x}{10000} \\[1em] = \dfrac{x}{125}$

The elder son spends 80% of his share, so he saves (100 - 80)% = 20% of his share.

Savings of the elder son = 20% of $\dfrac{x}{125}$

$= \dfrac{20}{100} \times \dfrac{x}{125} \\[1em] = \dfrac{20x}{12500} \\[1em] = \dfrac{x}{625}$

According to the given condition,

$\Rightarrow \dfrac{x}{625} = 60 \\[1em] \Rightarrow x = 60 \times 625 \\[1em] \Rightarrow x = 37500$

Hence, Imran's monthly income is ₹37,500.