Std 6 Mathematics · Chapter 13

13. Percentage

Solutions to Practice Set 13.1, Practice Set 13.2 and Exercise 13. Maharashtra State Board (Balbharati), Grade Six Mathematics.

About the chapter

Percent means "per hundred". A ratio with denominator 100 can be written as a percentage. In this chapter, we change fractions into percentages and percentages into fractions. We find the percentage of a number. We also solve word problems on percentage.

Key points

The symbol % is used for percent. 45/100 = 45%
To change a fraction into a percentage, make its denominator 100. Or multiply it by 100.
To change a percentage into a fraction, write it over 100 and reduce it.
100% means the whole quantity.
A percentage can be more than 100, like 125%.

Formulas and terms

a% = a/100
a% of b = b × a/100
What percent is a of b = a/b × 100
Subsidy – money given by the government to reduce the price of a thing.
Discount – the amount reduced from the price of a thing.

Practice Set 13.1

1Write the following ratios using the word 'percent' and the symbol ' % '.

(i) 71/100 – seventy-one percent – 71%
(ii) 45/100 – forty-five percent – 45%
(iii) 186/100 – one hundred eighty-six percent – 186%
(iv) 19/100 – nineteen percent – 19%

2Complete the following activities.

(i) 1/2 = 1 × 50/2 × 50 = 50/100 = 50 %

(ii) 5/4 = 5 × 25/4 × 25 = 125/100 = 125 %

3Convert the following percentages into fractions.

(i) 64 percent = 64/100 = 16/25
(ii) 91% = 91/100
(iii) 175% = 175/100 = 7/4 = 1 3/4
(iv) 16 2/3% = 50/3 ÷ 100 = 50/300 = 1/6
(v) 100% = 100/100 = 1

4Convert the following fractions into percentages.

(i) 2/5 = 2 × 20/5 × 20 = 40/100 = 40%
(ii) 3/8 = 3/8 × 100 = 300/8 = 37.5%
(iii) 5/4 = 5 × 25/4 × 25 = 125/100 = 125%
(iv) 1/16 = 1/16 × 100 = 100/16 = 6.25%
(v) 736/800 = 736 ÷ 8/800 ÷ 8 = 92/100 = 92%

Practice Set 13.2

1Find the given percentage of the given number.

(i) 80% of 125 = 125 × 80/100 = 100
(ii) 37% of 67 = 67 × 37/100 = 2479/100 = 24.79
(iii) 125% of 300 = 300 × 125/100 = 375
(iv) 87% of 1200 = 1200 × 87/100 = 1044

2Calculate what percent the first number is of the second number.

(i) 4, 10 → 4/10 × 100 = 40%
(ii) 44, 88 → 44/88 × 100 = 50%
(iii) 23, 92 → 23/92 × 100 = 25%
(iv) 60, 300 → 60/300 × 100 = 20%
(v) 215, 250 → 215/250 × 100 = 86%

3384 out of 400 students voted in the school cabinet election. Find (i) the voting percentage (ii) the percentage of students who did not vote.

(i) Voting percentage = 384/400 × 100 = 96%

(ii) Students who did not vote = 400 − 384 = 16
Percentage = 16/400 × 100 = 4%

96% students voted and 4% students did not vote.

4The price of a tractor is ₹5,50,000 and a 45% subsidy is given on it. How much subsidy is given?

Subsidy = 45% of 5,50,000
= 5,50,000 × 45/100
= 5,500 × 45 = ₹2,47,500

A subsidy of ₹2,47,500 is given.

5Jowar was sown in 75% of a field of area 19,500 square metres. In how many square metres was jowar sown?

Area of jowar = 75% of 19,500
= 19,500 × 75/100
= 195 × 75 = 14,625 sq m

Jowar was sown in 14,625 square metres.

6Kasturi bought a bag of organic fertilizer for ₹1,000 with a 15% discount. How much discount will she get on two such bags?

Discount on one bag = 1,000 × 15/100 = ₹150
Discount on two bags = 2 × 150 = ₹300

She will get a discount of ₹300 on two bags.

Exercise 13

1Choose the correct option.

(i) 10% of 500 = — (b) 50
500 × 10/100 = 50
(ii) The number 12 is … percent of 40 — (d) 30
12/40 × 100 = 30

2Solve and write the correct symbol among <, > or = in the box.

(i) 15% of 60 = 9 and 10% of 10 = 1
∴ 15 percent of 60 > 10 percent of 10

(ii) 20% of 10 = 2 and 10% of 20 = 2
∴ 20% of 10 = 10% of 20

(iii) 10% of 250 = 25 and 20% of 125 = 25
∴ 10 percent of 250 = 20 percent of 125

(iv) 30% of 160 = 48 and 40% of 150 = 60
∴ 30% of 160 < 40% of 150

3The number of malnourished people decreased from 1,20,00,000 to 90,00,000 in 5 years. Find the percentage decrease.

Decrease = 1,20,00,000 − 90,00,000 = 30,00,000
Percentage decrease = 30,00,000/1,20,00,000 × 100
= 1/4 × 100 = 25%

The number decreased by 25%.

4Out of 14,000 sugarcane seedlings, 700 were bad. i) How many seedlings were good? ii) What percent were good? iii) What percent were bad?

i) Good seedlings = 14,000 − 700 = 13,300

ii) Percentage of good seedlings = 13,300/14,000 × 100 = 95%

iii) Percentage of bad seedlings = 700/14,000 × 100 = 5%

5Meena needs 25 g of protein a day and gets 8 g from one glass of milk. What percent of her daily requirement is that?

Percentage = 8/25 × 100 = 800/25 = 32%

One glass of milk gives 32% of her daily protein need.

6Deepti got 11,484 votes, which was 44% of the total. Trupti got 26%. How many people did not vote for either of them?

44% of total votes = 11,484
1% of total votes = 11,484 ÷ 44 = 261
Total votes = 261 × 100 = 26,100

Percentage of votes to neither = 100 − (44 + 26) = 30%
Number of such people = 26,100 × 30/100 = 7,830

7,830 people did not vote for either of them.

7A cricket team played 20 matches, lost 40% of them and won the rest. How many did it win?

Matches lost = 20 × 40/100 = 8
Matches won = 20 − 8 = 12

The team won 12 matches.

i) What change would make the answer "15 matches won"?

If 15 matches are won, 5 matches are lost. 5/20 × 100 = 25%. So, change "lost 40%" to "lost 25%".

Matches lost = 20 × 25/100 = 5
Matches won = 20 − 5 = 15

ii) What change would increase the winning percentage by 10?

Now the team wins 60% of the matches. To make it 70%, change "lost 40%" to "lost 30%".

Matches lost = 20 × 30/100 = 6
Matches won = 20 − 6 = 14
Winning percentage = 14/20 × 100 = 70%

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