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RS Aggarwal 2019,2020 solution class 7 chapter 10 Percentage Exercise 10C

Exercise 10C

Page-148

Question 1:

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34 as rate per cent is

(a) 7.5%
(b) 75%
(c) 0.75%
(d) none of these

Answer 1:

(b) 75%

34 = (34×100)% = 75%


Question 2:

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The ratio 2 : 5 as rate per cent is

(a) 4%
(b) 0.4%
(c) 40%
(d) 14%

Answer 2:

(c) 40%

2 : 5 = 25 = (25×100)% = 40%


Question 3:

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813% expressed as a fraction, is

(a) 253
(b) 325
(c) 112
(d) 14

Answer 3:

(c) 112

813% = 253% = (253×1100)=(13×4)=112
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Question 4:

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If x% of 75 = 9, then the value of x is

(a) 16
(b) 14
(c) 12
(d) 8

Answer 4:

(c) 12
We have x% of 75 = 9
 (x100×75)=9
x = (9×10075)=12
Hence, the value of x is 12

Question 5:

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What per cent of 27 is 135?

(a) 25%
(b) 20%
(c) 15%
(d) 10%

Answer 5:

(d) 10%

Let x be the required percent.
Then, x % of 27 = 135
(x100×27)=135
x = (100×735×2) = 10
Hence, 10% of 27 is 135

Question 6:

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What per cent of 1 day is 36 minutes?

(a) 25%
(b) 2.5%
(c) 3.6%
(d) 0.25%

Answer 6:

(b) 2.5%

Let x % of 1 day be 36 min.
Then, (x100×1×24×60) min = 36 min
x = (36×10024×60) = (3×52×3)%=(52)%=2.5% 

Hence, 2.5% of 1 day is 36 min.

Question 7:

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A number increased by 20% gives 42. The number is

(a) 35
(b) 28
(c) 36
(d) 30

Answer 7:

(a) 35
Let the required number be x.
Then, x + 20% of x = 42
(x+20x100)=42
(x+x5)=42
(5x+x5)=42        [∵ LCM of 1 and 5 = 5]
(6x5)=42
x = (42×56)=35
Hence, the required number is 35.

Question 8:

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A number decreased by 8% gives 69. The number is

(a) 80
(b) 75
(c) 85
(d) none of these

Answer 8:

(b) 75
Let the required number be x.
Then, x − 8% of x = 69
(x-8x100) = 69
(x-2x25) = 69
⇒ (25x-2x25) = 69            [Since L.C.M. of 1 and 25 = 25]
(23x25)=69
x = (69×2523) = 75
Hence, the required number is 75

Question 9:

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An ore contains 5% copper. How much ore is required to obtain 400 g of copper?

(a) 2 kg
(b) 4 kg
(c) 6 kg
(d) 8 kg

Answer 9:

(d) 8 kg
Let x kg be the required amount of ore.
Then, 5% of x kg = 400 g = 0.4 kg        [∵ 1 kg = 1000 g]
(5100×x)=0.4
x = (0.4×1005) = 8
Hence, 8 kg of ore is required to obtain 400 g of copper.

Question 10:

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After deducting a commission of 10% a TV costs Rs 18000. What is its gross value?

(a) Rs 18800
(b) Rs 20000
(c) Rs 19800
(d) none of these

Answer 10:

(b) Rs. 20000
Suppose that the gross value of the TV is Rs x.
Commission on the TV = 10%
Price of the TV after deducting the commission = Rs (x − 10% of x)
                                                                  = Rs (x-10100x) = Rs (100x-10x100) = Rs (9x10)
However, price of the TV after deducting the commission = Rs 18000
Then, Rs (9x10) = Rs 18000
x = (18000×109) = Rs (2000 × 10) = Rs 20000
Hence, the gross value of the TV is Rs 20,000

Question 11:

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On increasing the salary of a man by 25%, it becomes Rs 20000. What was his original salary?

(a) Rs 15000
(b) Rs 16000
(c) Rs 18000
(d) Rs 25000

Answer 11:

(b) Rs. 16000
Let us assume that the original salary of the man is Rs x.
Increase in it = 25%
Value increased in the salary = 25% of Rs. x
                                               = Rs (25100×x) = Rs (x4)
Salary after increment= Rs (x+x4) = Rs (5x4)
However, increased salary = Rs 20000
Then, Rs (5x4) = Rs 20000
∴  x = Rs (20000×45) = Rs 16000
Hence, the original salary of the man is Rs 16,000

Question 12:

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In an examination, 95% of the total examinees passed. If the number of failures is 28, how many examinees were there?

(a) 600
(b) 480
(c) 560
(d) 840

Answer 12:

(c) 560
Suppose that the number of examinees is 100.
Number of passed examinees = 95
Number of failed examinees = (100 − 95) = 5

Total number of examinees if 5 of them failed = 100
Total number of examinees if 28 of them failed = (1005×28)=(20×28)=560
Hence, there were 560 examinees.

Question 13:

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A fruit-seller had some apples. He sells 40% of them and still has 420 apples. How many apples had he in all?

(a) 588
(b) 600
(c) 700
(d) 725

Answer 13:

(c) 700
Suppose that the fruit seller initially had 100 apples.
Number of apples sold = 40
∴ Number of remaining apples = (100 − 40) = 60

Initial number of apples if 60 of them are remaining = 100
Initial number of apples if 420 of them are remaining = (10060×420) = 700
Hence, the fruit seller originally had 700 apples with him.

Question 14:

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The value of a machine depreciated 10% annually. If its present value is Rs 25000, what will be its value after 1 year?

(a) Rs 27500
(b) Rs 22500
(c) Rs 25250
(d) none of these

Answer 14:

(c) Rs. 25250

Present value of the machine = Rs 25000
Decrease in its value after 1 year = 10% of Rs 25000
                                                      = Rs (10100×25000) = Rs 2500
Depreciated value after 1 year = Rs (25000 − 2500) = Rs 22500

Hence, the value of the machine after 1 year will be Rs 22500

Question 15:

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8% of a number is 6. What is the number?

(a) 48
(b) 96
(c) 75
(d) 60

Answer 15:

(c) 75

Let the required number be x. Then, we have:
8% of x = 6
(8100×x)=6
x = (6×1008)=75
Hence, the required number is 75

Question 16:

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60% of 450 = ?

(a) 180
(b) 210
(c) 270
(d) none of these

Answer 16:

(c) 270
60% of 450 = (60100×450)
                    = (35×450) = (3 × 90) = 270

Question 17:

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On reducing the value of a chair by 6% it becomes Rs 658. The original value of the chair is

(a) Rs 750
(b) Rs 720
(c) Rs 500
(d) Rs 700

Answer 17:

(d) Rs. 700
Let us assume that the original price of the chair is Rs x.
Reduce percentage on the chair = 6%
So, value of reduction on the chair = 6% of Rs. x
                                                        = Rs (6100×x) = Rs (3x50)
Reduced price of the chair = Rs (x-3x50)
                                            = Rs (50x-3x50) = Rs (47x50)
However, present price of the chair = Rs 658
Then, Rs (47x50) = Rs 658
⇒ Rs (47x50) = Rs 658
x = Rs (658×5047) = Rs (14×50)=700
Hence, the original price of the chair is Rs 700

Question 18:

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70% of students in a school are boys. If the number of girls is 240, how many boys are there in the school?

(a) 420
(b) 560
(c) 630
(d) 480

 

Answer 18:

(b) 560

Let the total number of students be 100.
Then, number of boys = 70
∴ Number of girls = (100 − 70) = 30

Now, total number of students if there are 30 girls = 100
Total number of students if there are 240 girls = (10030×240)=800
∴ Number of boys = (800 − 240) = 560

Hence, there are 560 boys in the school.

Question 19:

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If 11% of a number exceeds 7% of the number by 18, the number is

(a) 72
(b) 360
(c) 450
(d) 720

Answer 19:

(c) 450

Let x be the number.
(11% of x) − (7% of x) = 18
(11x100-7x100)=18
4x100=18
x = (18×1004)=(18×25)=450
Hence, the required number is 450

Question 20:

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If 35% of a number added to 39 is the number itself, the number is

(a) 60
(b) 65
(c) 75
(d) 105

Answer 20:

(a) 60
Let x be the number.
According to question, we have:
(35% of x ) + 39 = x
(35100×x)+39=x
(7x20)+39=x
(x-7x20)=39
(20x-7x20)=39
(13x20)=39
x = (39×2013) = 60
Hence, the required number is 60

Question 21:

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In an examination it is required to get 36% to pass. A student gets 145 marks and fails by 35 marks. The maximum marks are

(a) 400
(b) 450
(c) 500
(d) 600

Answer 21:

(c) 500
Let x be the maximum marks.
Pass marks = (145 + 35) = 180
∴ 36% of x = 180
(36100×x)=180
x = (180×10036)=(5×100)=500
Hence, maximum marks = 500

Page-150

Question 22:

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A number decreased by 40% gives 135. The number is

(a) 175
(b) 200
(c) 250
(d) 225

Answer 22:

(d) 225
Let x be the number.
According to question, we have:
x − 40% of x = 135
(x-40x100)=135
(100x-40x100)=135
(60x100)=135
x = (135×10060) = 225
Hence, the required number is 225

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