Thursday, December 13, 2012

CBSE Class 7 - Maths - CH8 - Comparing Quantities (Percentage, Ex 8.2)

Comparing Quantities 
(Percentage)

Important Points

1. Per cent is derived from Latin word ‘per centum’ meaning ‘per or out of hundred
2. 25% = 25 out of hundred = 25/100 = 1/4 = 0.25
3. Graphically it can be represented as shown.
4.Fractions and decimals can be converted to percentages and vice versa.

Q1: Convert the following to per cents:





Answer:

















NCERT Exercise 8.2

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 = 1 × 100 / 8 = 12.5%

(b) 5/4 = 5 × 100/4 = 125%

(c) 3/40 = 3 × 100/40 = 30/4 = 7.25%





Q2: Convert the given decimal fractions to per cents.
(a) 0.65 (b) 2.1 (c) 0.02 (d) 12.35

Answer:


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


Answer:
(i) Total Parts = 4
    Filled part = 1
    Filled part in fraction = 1/4
    % of Filled part = (1/4) × 100 = 100/4 = 25%

(ii) Total Parts = 5
    Filled parts = 3
    Filled parts in fraction = 3 out of 5 = 3/5
    Filled parts in percent = (3/5) × 100 = 3 × 20 = 60%

(iii) Total parts = 8
    Filled parts  = 3
    Filled parts in fraction = 3/8
    Filled parts in percent = (3/8) × 100 = 3 × 12.5 = 37.5%

Q4: Find: (a) 15% of 250 (b) 1% of 1 hour (c) 20% of Rs 2500 (d) 75% of 1 kg

Answer
(a) 15% of 250
    = (15/100) of 250 = (15/100)  × 250 
    = 15 × 25/10 = 375/10 = 37.5

(b) 1% of 1 hour 
   = (1/100) of 1 hour 
   = (1/100) × 3600 seconds                                   (∵ 1 hour =  3600 seconds)
   = 36 seconds
   
(c) 20% of Rs 2500
   = (20/100) of 2500
   = (20/100) × 2500
   = 20 × 25 = Rs 500

(d) 75% of 1 kg
  = (75/100) of 1 kg
  = (75/100) × 1 
  = 0.75 kg
 (∵ 1 kg =  1000 grams)
  = 0.75  × 1000g = 750g

Q5: Find the whole quantity if
(a) 5% of it is 600. (b) 12% of it is Rs 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 it is 600.
⇒ 5% of n = 600
⇒ (5/100) of n = 600
⇒ (5/100) × n = 600
⇒  n = 600 × (100/5) = 600 × 20 = 12000

(b) 12% of it is Rs 1080.
⇒ 12% of n = 1080
⇒  (12/100) of n = 1080
⇒  (12/100) × n =  1080
⇒  n = 1080 × (100/12) = 90 × 100 = ₹ 9000


(c) 40% of it is 500 km
⇒ 40% of y = 500
⇒ (40/100) of y = 500
⇒  (4/10) × y = 500
⇒  y = 500 × (10/4) = 125 × 10 = 1250 km

(d) 70% of it is 14 minutes.
⇒ 70% of t = 14 mins
⇒ (70/100) of t = 14
⇒ (7/10) × t = 14
⇒  t = 14 × (10/7) = 2 × 10 = 20 minutes

(e) 8% of it is 40 litres
⇒ 8% of n = 40
(8/100) of n = 40
⇒ (8/100) × n = 40
⇒ n = 40 × (100/8) = 5 × 100 = 500 litres

Q6: Convert given per cents to decimal fractions and also to fractions in simplest forms:
      (a) 25% (b) 150% (c) 20% (d) 5%

Answer:
(a) 25% = 25/100 = 0.25
              = 25/100 = 1/4

(b) 150% = 150/100 = 15/10 = 3/2 = 1.5

(c) 20% = 20/100 = 2/10 = 1/5 = 0.20

(d) 5% = 5/100 = 1/20 = 0.05


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

Answer: Number of females in city = 30%
    Number of males in city = 40%
    Number of children in city = x%
    ∴ Females % + Males % + Children % = 100% (Total population of city)
    ∴ 30% + 40% + x% = 100%
    ∴ 70% + x% = 100%
    ∴ x% = 100 - 70 = 30%
    ∴ Children are 30% of the total population.

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: Let the total voters = 100%
                Voters who voted in % = 60%
 ⇒   Percentage of voters who did not vote = 100 - 60 = 40%
       Total Voters  = 15000
 ⇒  40% of 15000 did not vote = 40% of 15000
             = (40/100) of 15000
             = (4/10) × 1500 
             = 4 ×150 = 6000
 Thus 40% voters i.e. 6000 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 =  ₹ n
       Given, she saves 10% of her salary = ₹ 400
⇒    10% of n = 400
⇒     (10/100) of n = 400
⇒     (1/10) × n = 400
⇒      n = 400 × (10/1) = 4000
Thus Meeta's salary is ₹4000

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

Answer:  Total matches played = 20
  Winning % = 25%
  ⇒ Matches won = 25% of 20 
            = (25/100) of 20
            = (1/4) × 20 = 5
Thus local cricket team won 5 matches.


Miscellaneous Questions

Q11: In a school having strength of 740 students, 35% study French. How many do not learn French.

Answer: Total number of students = 740
           Number of students learn French = 35%
∴ Number of students who do not study French = 100 - 35 = 65%
∴ Actual number of students not studying French = 65% of 740
              = 65% of 740
              = (65/100) of 740
              = (13/20) × 740 
              = 13 × 37 
              = 481
Thus 481 students do not study French.

Q12: Decrease 300 by 24%

Answer:  Decrease 300 by 24%
 
∴ New value is = (100 -24)% of 300
        = 76% of 300
        = (76/100) of 300
        = (76/100) × 300
        = 76 × 3 
        = 228


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