Q1: Convert the given fractional numbers to percent:
(a) 1/8
(b) 5/4
(c) 3/40
(d) 2/7
Ans: To convert the given fraction into percent we multiply the fraction by 100 and put the percent (%) Sign :
Q2: Convert the given decimal fractions to per cents:
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Ans: To convert the decimals into percent, first convert them into fraction and then multiply by 100 and put percent sign.
(a) 0.65:
0.65 can be written as 65/100.
To convert it to a percentage, we multiply it by 100.
(65/100) * 100 = 65%
Therefore, 0.65 is equal to 65%.
(b) 2.1:
2.1 remains the same.
To convert it to a percentage, we multiply it by 100.
2.1 * 100 = 210%
Therefore, 2.1 is equal to 210%.
(c) 0.02:
0.02 can be written as 2/100.
To convert it to a percentage, we multiply it by 100.
(2/100) * 100 = 2%
Therefore, 0.02 is equal to 2%.
(d) 12.35:
12.35 remains the same.
To convert it to a percentage, we multiply it by 100.
12.35 * 100 = 1235%
Therefore, 12.35 is equal to 1235%.
Q3: Estimate what part of the figures is coloured and hence find the percent which is coloured.
Ans: (i) We can observe that only 1 part is coloured out of 4 parts.
Therefore, Coloured part = 1/4
∴ Percent of coloured part =
(ii) We can observe that only 3 parts is coloured out of 5 parts.
Therefore, Coloured part = 3/5
∴ Percent of coloured part
(iii) We can observe that only 3 parts is coloured out of 8 parts.
Therefore, Coloured part = 3/8
∴ Percent of coloured part
= 37.5%
Q4: Find:
(a) 15% of 250
(b) 1% of 1 hour
(c) 20% of 2500
(d) 75% of 1 kg
Ans:
(a) 15% of 250
(b) We know that, 1 hour = 60 minutes = 60 x 60 seconds = 3600 seconds
1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60] second
(c) 20% of Rs 2500
(d) 75% of 1 kg = 75% of 1000 g
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
Ans: Let the whole quantity be x in given questions:
Q6: Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Ans:
S. No.  Per cents  Fractions  Simplest form  Decimal form 
(a)  25%  25/100  1/4  0.25 
(b)  150%  150/100  3/2  1.5 
(c)  20%  20/100  1/5  0.2 
(d)  5%  5/100  1/20  0.05 
Q7: In a city, 30% are females, 40% are males and remaining are children. What percent are children?
Ans:
Given:
Percentage of females = 30%
Percentage of males = 40%
Total percentage of females and males = 30 + 40 = 70%
Percentage of children = Total percentage  Percentage of males and females
= 100%  70%
= 30%
Hence, 30% are children.
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?
Ans: Total voters = 15,000
Percentage of voted candidates = 60%
Percentage of not voted candidates = 100  60 = 40%
Actual candidates, who did not vote = 40% of 15000
Hence, 6,000 candidates did not vote.
Q9: Meeta saves Rs 4000 from her salary. If this is 10% of her salary. What is her salary?
Ans: Let Meera's total salary be Rs x.
Now, 10% of salary = Rs 4000
⇒ 10% of x = Rs 400
⇒ (10/100) * x = Rs 4000
⇒ x = (4000 * 100)/10 = Rs 40,000
Hence, Meera's salary is Rs 40,000.
Q10: A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Ans: Number of matches played by cricket team = 20
Percentage of won matches = 25%
Total matches won by them = 25% of 20
Hence, they won 5 matches.
Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
(a) Gardening shears bought for ₹250 and sold for ₹325.
(b) A refrigerator bought for ₹12,000 and sold at ₹13,500.
(c) A cupboard bought for ₹2,500 and sold at ₹3,000.
(d) A skirt bought for ₹250 and sold at ₹150.
2. Convert each part of the ratio to percentage:
(a) 3 : 1
(b) 2 : 3 : 5
(c) 1 : 4
(d) 1 : 2 : 5
3. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
4. Arun bought a car for ₹3,50,000. The next year, the price went up to ₹3,70,000. What was the Percentage of price increase?
5. I buy a T.V. for ₹10,000 and sell it at a profit of 20%. How much money do I get for it?
6. Juhi sells a washing machine for ₹13,500. She loses 20% in the bargain. What was the price at which she bought it?
7. (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?
8. Amina buys a book for ₹275 and sells it at a loss of 15%. How much does she sell it for?
9. Find the amount to be paid at the end of 3 years in each case:
(a) Principal = ₹1,200 at 12% p.a.
(b) Principal = ₹7,500 at 5% p.a.
10. What rate gives ₹280 as interest on a sum of ₹56,000 in 2 years?
Interest (I): ₹45
Rate (R): 9%
Time (T): 1 year
Using the formula for Simple Interest: $I=\frac{P}{\times}I\; =\; \backslash frac\{P\; \backslash times\; R\; \backslash times\; T\}\{100\}$
$\frac{45}{\times}=P\backslash frac\{45\; \backslash times\; 100\}\{9\; \backslash times\; 1\}\; =\; P$
$P=\u20b9500P\; =\; \u20b9500$
Q1: Find the ratio of:
(a) Rs5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Ans: To find ratios, both quantities should be in same unit.
(a) Rs 5 to 50 paise
⇒ 5 x 100 paise to 50 paise [∴ Rs 1 = 100 paise]
⇒ 500 paise to 50 paise
Thus, the ratio is = 500/50 = 10/1 = 10 : 1
(b) 15 kg to 210 g
⇒ 15 x 1000 g to 210 g [∵ 1kg = 1000 g]
⇒ 15000 g to 210 g
Thus, the ratio is = 15000/210 = 500/7 = 500:7
(c) 9 m to 27 cm
⇒ 9 x 100 cm to 27 cm [∵ 1m = 100 cm]
⇒ 900 cm to 27 cm
Thus, the ratio is = 900/27 = 100/3 = 100:3
(d) 30 days to 36 hours
⇒ 30 x 24 hours to 36 hours [∵ 1 day = 24 hours]
⇒ 720 hours to 36 hours
Thus, the ratio is = 720/36 = 20/1 = 20:1
Q2: In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Ans:
∵ 6 students need = 3 computers
∵ 1 student needs = 3/6 computers
Therefore, 24 students need =
Thus, 12 computers will be needed for 24 students.
Q3: Population of Rajasthan = 570 lakhs and population of U.P. = 1660 lakhs. Area of Rajasthan = 3 lakh km2 and area of U.P. = 2 lakh km2.
(i) How many people are there per km2 in both states?
(ii) Which state is less populated?
Ans:
(ii) By comparing the above two states we can clearly observe that Rajasthan is less populated.
76 videos345 docs39 tests

1. How can I compare quantities using ratios and proportions? 
2. What is the difference between direct and inverse proportions when comparing quantities? 
3. How can I calculate the percentage increase or decrease when comparing quantities? 
4. Can I compare quantities using fractions instead of ratios? 
5. What are some reallife examples where comparing quantities is important? 

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