8th Maths : Chapter 4 : Life Mathematics : Percentage : Exercise 4.1 : Text Book Back Exercises Questions with Answers, Solution

**Exercise
4.1**

** **

**1. Fill in the blanks:**

(i) If 30 % of *x* is 150, then *x* is _________.
**[Answer: 500]**

**Solution:**

Given 30% of *x* is 150

i.e 30/100 × *x* = 150

∴ *x* = [150 × 100] / 30

∴ *x* = 500

(ii) 2 minutes is _________ % to an hour.
**[Answer: 3 1/3 %]**

**Solution:**

Let 2 min be *x* % of an hour

and 1 hr = 60 min

*x* % = (2/60) × 100 = 200 / 60 = 10 /
3 = 3 (1/3)

*x* = 3 (1/3)%

(iii) If *x* % of *x* = 25, then *x* = ________. **[Answer: 50]**

**Solution:**

Given that *x* % of *x* is 25

∴ [*x* / 100] × *x* = 25

∴ *x*^{2} = 25 × 100 = 2500

∴ *x* = √2500 = 50

(iv) In a school of 1400 students, there
are 420 girls. The percentage of boys in the school is ________. **[Answer: 70]**

**Solution:**

Given total number of students in school = 1400

Number of girls in school = 420

∴ Number of boys in school = 1400 − 420 = 980

% of boys in school = [ Number of boys / Total number of
students ] × 100 = [ 980 / 1400 ] × 100

= 980 / 14 = 70

% of boys = 70%

(v) 0.5252 is ________ % . **[Answer: 52.52%]**

**Solution:**

Given a number, and to express as a percentage, we need to
multiply by 100

∴ to express 0.5252 as percentage, we should multiply by 100

∴ 0.5252 × 100 = 52.52%

** **

**2. Rewrite each underlined part using
percentage language.**

**(i) One half of the cake is distributed
to the children.**

**Solution:**

One half is nothing but 1/2

as percentage, we need to multiply by 100

∴ 1/2 × 100 = 50%

**[Answer: 50% of the cake is distributed to the children]**

**(ii) Aparna scored 7.5 points out of
10 in a competition.**

**Solution:**

7.5 points out of 10 is 7.5/10 = 0.75

For percentage, we need to multiply by 100

∴ We get 0.75 × 100 =
75%

**[Answer: Aparna scored 75% in a competition]**

**(iii) The statue was made of pure silver.**

**Solution:**

Pure silver means there are no other metals

so,100 out of 100 parts is made of silver = 100/100

∴ to express as
percentage, [100 / 100] × 100% = 100%

**[Answer: The statue was made of 100% silver ]**

**(iv) 48 out of 50 students participated
in sports.**

48 out of 50 students in fraction form is 48/50.

As a percentage, we need to multiply by 100

∴ [48/50] × 100 = 96%

**[Answer: 96% students participated in sports]**

**(v) Only 2 persons out of 3 will be
selected in the interview.**

**Solution:**

2 out of 3 in fraction form is 2/3

to express as percentage, we need to multiply by 100

(2/3) × 100 = 200/3 = 66
2/3%

**[Answer: only 66 2/3% persons will be selected in the interview]**

** **

**3. 48 is 32% of which number?**

**Solution:**

Let the number required to be found be ‘*x*’

Given that 32% of *x* is 48

ie (32/100) × *x* = 48 ∴ *x* = [48 × 100] / 32 = 300 / 2 = 150 ∴ *x* =
150

** **

**4. What is 25% of 30% of 400?**

**Solution:**

Required to find 25% of 30% of 400

First 30% of 400 = [30/100] × 400 = 120

Next 25% of the above is = [25/100] × 120 = **30**

** **

**5. If a car is sold for ₹200000 from
its original price of ₹300000, then find the percentage of decrease in the value
of the car.**

**Solution:**

original price of car = ₹ 3,00,000

actual selling price of car = ₹ 2,00,000

Decrease in amount from original = 3,00,000 − 2,00,000 =
1,00,000

Percentage decrease = [ Decrease / Original value ] × 100 = [ 1,00,000 / 3,00,000 ] × 100 = 100 / 3 = **33 1/3%**

** **

**6. If the difference between 75% of a
number and 60% of the same number is 82.5, then find 20% of that number.**

**Solution:**

Given that 75% of number less 60% of number is 82.5

Let the number be ‘*x*’

∴ (75/100) × *x* – (60/100)
× *x* = 82.5

∴ 0.75 *x* – 0.60 *x*
= 82.5

∴ 0.15 *x *= 82.5

∴ *x *= 82.5 / 0.15 = 8250 / 15 = 550

Required to find 20% of number ie 20% of *x*.

(20/100) × *x* = (20/100) × 550 = **110**

** **

**7. A number when increased by 18% gives
236. Find the number.**

**Solution 1:**

Let the number be *x*. Given that when it is increased by
18%, we get 236.

Solution 2:

Let the number be *x*. Given that when it is increased by 18%, we get 236.

*x* + (18/100)*x* = 236

( 100*x* + 18*x* ) / 100 = 236

∴ 118/100 *x *= 236

∴ the number = *x *= [236 × 100] / 118 = 200

** **

**8. A number when decreased by 20% gives
80. Find the number.**

**Solution 1:**

Let the number be *x*. Given that when it is increased by
20% we get 80.

Solution 2:

Let the number be *x*. Given that when it is increased by 20% we get 80.

*x* – [ (20/100) × *x* ] = 80

[100*x* – 20*x*] / 100 = 80

80*x* / 100 = 80 ⇒ *x *= [80 × 100] / 80

*x *= 100

** **

**9. A number is increased by 25% and then
decreased by 20%. Find the percentage change in that number.**

**Solution: **

**Method 1**

Let the number be *x*.

First it is increased by 25%

∴ It becomes *x* +
(25/100) × *x* = (125/100) *x*

Secondary it is decreased by 20%

[125*x* / 100] – [20 / 100] × [125/100]*x* = [125/100]*x*
× [80/100] = *x*

Now we get back *x*, therefore there is no change.

Hence percentage change in that number is 0%

**Method 2**

[to understand, let us assume that number is 100]

So, first when we increase by 25%, we get

100 + ( [25 /100] × 100 ) = 100 +25 = 125

Now this 125 is decreased by 20%, we get

125 – ([25/100] × l25) = 125 − 25 = 100

∴ We get back 100 ⇒ No change

Hence percentage change in that number is 0%

** **

**10. The ratio of boys and girls in a
class is 5:3. If 16% of boys and 8% of girls failed in an examination, then find
the percentage of passed students.**

Solution 1:

**Solution 2: **

Let number of boys be ‘*b*’ and number of girls be ‘*g*’

Ratio of boys and girls is given as 5:3

*b*:*g* = 5:3 ⇒ *b*/*g* = 5/3
……..(A)

Failure in boys = 16% = 16/100 × *b* = 16*b* / 100

Failure in girls = 8% = 8/100 × *g* = 8*g*/100

Pass in boys = 100 − 16% = 84% = 84/100 *b *……..(1)

Pass in girls = 100 − 8% = 92% = 92/100 *g *……..(2)

From A, we have *b*/*g* = 5/3, adding 1 on both sides,
we get

*b*/*g* + 1 = 5/3 + 1

[*b* + *g* ] / *g* = [5 + 3] / 3 = 8/3

∴ * g* = 3/8 (*b* + *g* ) ……..(3)

Similarly *b* = 5/8* *(*b* + *g* ) ……..(4)

Total pass = Pass in girls / Pass in boys

= (1) + (2) = (84/100) *b * + (92/100) *g*

Total pass percentage = [ **Total pass / Total students ]** ×
100

Total pass = boys passed + girls passed = {[(84/100)*b *+ (92/100)*g*
] / [*b* + *g*]} × 100

Substituting (3) & (4) in the above, we get

= {[(84/100)*b *+ (92/100)*g* ] / [*b* + *g*]}
× 100

= { [ ( 84/100 × 5/8(*b* + *g*) ) / (*b* + *g*)]*
*+ [ (92/100 × 3/8 (*b* + *g*) ) / (*b* + *g*) ] } × 100

= [ 84/100 × 5/8 ] + [ 92/100 × 3/8 ] = [420/800 + 276/800] ×
100

= 696/800 × 100 = 87%

Pass percentage = **87%**

** **

**Objective
Type Questions**

**11. 12% of 250 litre is the same as ________of
150 litre.**

(A)
10%

(B)
15%

(C)
20%

(D)
30%

**[Answer: (C) 20%]**

**Solution:**

12% of 250 = 12/100 × 250 = 30 lit.

Percentage : 30/100 × 100 =** 20%**

**12. If three candidates A, B and C in
a school election got 153,245 and 102 votes respectively, then the percentage of
votes got by the winner is___________.**

(A) 48%

(B) 49%

(C) 50%

(D) 45%

**[Answer: (B) 49%]**

**Solution:**

Candidate 1: 153

Candidate 2: 245 − winner [as maximum votes]

Candidate 3: 102

Total votes = 1 + 2 + 3 = 153 + 245 + 102 = 500

% of votes for winner = [ no. of votes that winner got / total
votes ] × 100

= [245 / 500] × 100 = **49%**

**13. 15% of 25% of 10000 =___________.
**

(A) 375

(B) 400

(C) 425

(D) 475

**[Answer: (A) 375]**

**Solution:**

15% of 25% of 10000 is

First let us do 25% of 10,000, which is

[25/100] × 10000 = 2500

Next 15% of the above is [15/100] × 2500 = **375**

**14. When 60 is subtracted from 60% of
a number to give 60, the number is**

(A) 60

(B) 100

(C) 150

(D) 200

**[Answer: (D) 200]**

**Solution:**

Let the number be ‘*x*’

60% of the number is (60/100) × *x* = 60*x* / 100

Given that when 60 is subtracted from 60%, we get 60

i.e (60/100)*x* − 60 = 60

∴ (60/100)*x* = 60 +
60 = 120

∴ *x* = [120 × 100] / 60 =** 200**

**15. If 48% of 48 = 64% of x , then x = **

(A) 64

(B) 56

(C) 42

(D) 36

**[Answer: (D) 36]**

**Solution:**

Given that 48% of 48 = 64% of *x*

[48/100] × 48 = [64/100] × *x*

*x* = [48 × 48] / 64 = 36

*x* = **36**

**Answer:**

**Exercise 4.1**

**1. (i) x = 500 (ii) 3 1/3 % (iii) x = 50 (iv) 70% (v) 52.52% **

**2. (i) 50% (ii) 75%
(iii) 100% (iv) 96% (v) 66 2/3% **

**3. x = 150 **

**4. 30 **

**5. 33 1/3%**

**6. 110 **

**7. x = 200 **

**8. x = 100 **

**9. No change**

**10. 87% **

**11. (C) 20% **

**12. (B) 49% **

**13. (A) 375 **

**14. (D) 200 **

**15. (D) 36**

Tags : Questions with Answers, Solution | Life Mathematics | Chapter 4 | 8th Maths , 8th Maths : Chapter 4 : Life Mathematics

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8th Maths : Chapter 4 : Life Mathematics : Exercise 4.1 (Percentage) | Questions with Answers, Solution | Life Mathematics | Chapter 4 | 8th Maths

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