**Exercise 8.1 :** Solutions of Questions on Page Number :** 157**

**Q1 : Find the ratio of:**

**(a) Rs 5 to 50 paise **

**(b) 15 kg to 210 g**

**(c) 9 m to 27 cm **

**(d) 30 days to 36 hours**

**Answer :**

(a) Rs 5 to 50 paise

1 rupee = 100 paise

5 rupee = 500 paise

Hence, the required ratio is 10:1.

(b) 15 kg to 210 g

1 kg = 1000 g

15 kg = 15000 g

Hence, the required ratio is 500:7.

(c) 9 m to 27 cm

1 m = 100 cm

9 m = 900 cm

Hence, the required ratio is 100:3.

(d) 30 days to 36 hours

1 days = 24 hrs

30 days = 24 × 30 = 720 hrs

Hence, the required ratio is 20:1.

**Q2 : In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?**

**Answer :**

For 6 students, number of computers required = 3

∴ For 1 student, number of computers required = 3/6 = 1/2

∴ For 24 students, number of computers required = 24 * 1/2= 12

Hence, 12 computers are required for 24 students.

**Q3 : Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.**

**Area of Rajasthan = 3 lakh km2 and area of UP = 2 lakh km2.**

**(i) How many people are there per km2 in both these States?**

**(ii) Which State is less populated?**

**Answer :**

(i) Population of Rajasthan in 3 km2 area = 570 lakh

Population of Rajasthan in 1 km2 area = 570 /3 = 190 lakh

Population of U.P in 2 km2 area = 1660 lakh

Population of U.P in 1 km2 area = 1660 / 2 = 830 lakh

(ii) It can be observed that population per km2 area is lesser for Rajasthan. Therefore, Rajasthan is less populated.

**Exercise 8.2 :** Solutions of Questions on Page Number : **164**

**Q1 : Convert the given fractional numbers to per cents.**

**(a) 1/ 8**

**(b) 5/4**

**(c) 3/ 40**

** (d) 2/7**

**Answer :**

(a) 1/ 8

(b) 5/4

(c) 3/ 40

(d) 2/7

**Q2 : Convert the given decimal fractions to per cents.**

**(a) 0.65 **

**(b) 2.1 **

**(c) 0.02 **

**(d) 12.35**

**Answer :**

(a) 0.65

(b)2.1

(c) 0.02

(d) 12.35

**Q3 : Estimate what part of the figures is coloured and hence find the per cent which is coloured.**

**Answer :**

(i) Here, 1 part out of 4 equal parts are shaded which represents the fraction .

(ii) Here, 3 parts out of 5 equal parts are shaded which represents the fraction .

(iii) Here, 3 parts out of 8 equal parts are shaded which represents the fraction.

**Q4 : Find:**

**(a) 15% of 250 **

**(b) 1% of 1 hour**

**(c) 20% of Rs 2500 **

**(d) 75% of 1 kg**

**Answer :**

(a)

(b) 1 hour = 60 minutes

(c)

(d)

**Q5 : Find the whole quantity if**

**(a) 5% of it is 600 **

**(b) 12% of it is 1080**

**(c) 40% of it is 500 km **

**(d) 70% of it is 14 minutes**

**(e) 8% of it is 40 litres**

**Answer :**

(a) 5% of x = 600

(b) 12% of x = Rs 1080

(c) 40% of x = 500 km

(d) 70% of x = 14 min

(e) 8% of x = 40 L

= 500 L

**Q6 : Convert given percents to decimal fractions and also to fractions in simplest forms:**

**(a) 25% **

**(b) 150%**

**(c) 20% **

**(d) 5%**

**Answer :**

(a) 25%

(b) 150%

(c) 20%

(d) 5%

**Q7 : In a city, 30% are females, 40% are males and remaining are children. What per cent are children?**

**Answer :**

It is given that 30% are females and 40% are males.

Children = (100 – 30 – 40) % = 30%

**Q8 : Out of 15, 000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?**

**Answer :**

Percentage of voters who voted = 60%

Percentage of those who did not vote = 100% – 60% = 40%

Number of people who did not vote = 40% of 15000

Therefore, 6000 people did not vote.

**Q9 : Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?**

**Answer :**

Let Meeta’s salary be Rs x.

Given that,

10% of x = 400

x = 400 × 10 = Rs 4000

Therefore, Meeta’s salary is Rs 4000.

**Q10 : A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?**

**Answer :**

Number of games won = 25% of 20

Therefore, the team won 5 matches.

**Exercise 8.3 :** Solutions of Questions on Page Number : **171**

**Q1 : Tell what is the profit or loss in the following transactions. Also find profit**

**percent or loss percent in each case.**

**(a) Gardening shears bought for Rs 250 and sold for Rs 325.**

**(b) A refrigerator bought for Rs 12,000 and sold at Rs 13,500.**

**(c) A cupboard bought for Rs 2,500 and sold at Rs 3,000.**

**(d) A skirt bought for Rs 250 and sold at Rs 150.**

**Answer :**

(a) Cost price = Rs 250

Selling price = Rs 325

Profit = 325 – 250 = Rs 75

== 30%

(b) Cost price = Rs 12000

Selling price = Rs 13,500

Profit = 13500 – 12000 = Rs 1500

Profit % = = 12.5%

(c) Cost price = Rs 2500

Selling price = Rs 3000

Profit = 3000 – 2500 = Rs 500

Profit % == 20%

(d) Cost price = Rs 250

Selling price = Rs 150

Loss = 250 – 150 = Rs 100

Loss % = = 40%

**Q2 : Convert each part of the ratio to percentage:**

**(a) 3:1 **

**(b) 2:3:5 **

**(c) 1:4 **

**(d) 1:2:5**

**Answer :**

(a) 3: 1

Total parts = 3 + 1 = 4

1st part

2nd part =

(b) 2: 3: 5

Total parts = 2 + 3 + 5 = 10

1st part =

2nd part =

3rd part =

(c) 1: 4

Total parts =1 + 4 = 5

1st part =

2nd part =

(d) 1: 2: 5

Total parts = 1 + 2 + 5 = 8

1st part =

2nd part =

3rd =

**Q3 : The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.**

**Answer :**

Initial population = 25000

Final population = 24500

Decrease = 500

% decrease =

**Q4 : Arun bought a car for Rs 3,50,000. The next year, the price went upto**

**Rs 3,70,000. What was the percentage of price increase?**

**Answer :**

Initial price = Rs 350000

Final price = Rs 370000

Increase = Rs 20000

% increase =

= %

**Q5 : I buy a T.V. for Rs 10,000 and sell it at a profit of 20%. How much money do I get for it?**

**Answer :**

Cost price = Rs 10000

Profit = 20% of 10000

= Rs 2000

Selling price = Cost price + Profit

= 10000 + 2000 = Rs 12,000

**Q6 : Juhi sells a washing machine for Rs 13, 500. She loses 20% in the bargain. What was the price at which she bought it?**

**Answer :**

Selling price = Rs 13500

Loss % = 20%

Let the cost price be x.

∴ Loss = 20% of x

Cost price – Loss = Selling price

= 16875

Therefore, she bought it for Rs 16875.

**Q7 : (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.**

**(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?**

**Answer :**

(i) Ratio of calcium, carbon, and oxygen = 10: 3: 12

As 10 + 3 +12 = 25,

Therefore, percentage of carbon = = 12%

(ii) Let the weight of the stick be x g.

12 % of x = 3

**Q8 : Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it for?**

**Answer :**

Cost price = Rs 275

Loss % = 15%

Loss = 15% of 275

Cost price – Loss = Selling price

275 – 41.25 = Selling price

Selling price = Rs 233.75

**Q9 :Find the amount to be paid at the end of 3 years in each case:**

**(a) Principal = Rs 1,200 at 12% p.a.**

**(b) Principal = Rs 7,500 at 5% p.a.**

**Answer :**

(a) Principal (P) = Rs 1200

Rate (R) = 12 % p.a.

Time (T) = 3 years

= Rs 432

Amount = P + S.I.

= 1200 + 432

= Rs 1632

(b) P = Rs 7500

R = 5% p.a.

T = 3 years

= Rs 1125

Amount = 7500 + 1125

= Rs 8625

**Q10 : What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?**

**Answer :**

Therefore, 0.25% gives Rs 280 as interest on the given sum.

**Q11 : If Meena gives an interest of Rs 45 for one year at 9% rate p.a.. What is the sum she has borrowed?**

**Answer :**

= Rs 500

Therefore, she borrowed Rs 500.