Percentage
- The value of a machine depreciates every year by 10%. If its present value is ₹ 50,000 then the value of the machine after 2 years is _________.
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Using Rule 18,
Required value= 50000 
1 - 10 
2 100 = 50000 9 × 9 = ₹ 40500 100 Correct Option: D
Using Rule 18,
Required value= 50000 1 - 10 2 100 = 50000 9 × 9 = ₹ 40500 100
- In an election between two candidates, 75% of the voters cast their votes, out of which 2% votes were declared invalid. A candidate got 9261 votes which were 75% of the valid votes. The total number of voters enrolled in that election was
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Let the total number of voters enrolled be x.
Number of votes polled= 75% of x = 3x 4
Number of valid votes= 3x - 2 × 3x 4 100 4 = 3x - 3x 4 200 = 147x 200 Now, 75% of 147x = 9261 200 or 3 of 147x = 9261 4 200 or x = 9261 × 4 × 200 = 16800 3 × 147 Correct Option: C
Let the total number of voters enrolled be x.
Number of votes polled= 75% of x = 3x 4
Number of valid votes= 3x - 2 × 3x 4 100 4 = 3x - 3x 4 200 = 147x 200 Now, 75% of 147x = 9261 200 or 3 of 147x = 9261 4 200 or x = 9261 × 4 × 200 = 16800 3 × 147
- A man spends 75% of his income. His income increases by 20% and his expenditure also increases by 10%. The percentage of increase in his savings is
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Man’s income = ₹ 100 (let)
Expenditure = ₹ 75
Savings = ₹ 25New income = 100 × 120 = ₹120 100 New expenditure = 75 × 110 = ₹ 82.5 100
Savings = 120 – 82.5 = ₹ 37.5
Increase in savings = 37.5 – 25 = ₹ 12.5
∴ Increase per cent= 12.5 × 100 = 50% 25 Correct Option: C
Man’s income = ₹ 100 (let)
Expenditure = ₹ 75
Savings = ₹ 25New income = 100 × 120 = ₹120 100 New expenditure = 75 × 110 = ₹ 82.5 100
Savings = 120 – 82.5 = ₹ 37.5
Increase in savings = 37.5 – 25 = ₹ 12.5
∴ Increase per cent= 12.5 × 100 = 50% 25
- If each side of a cube is increased by 10% the volume of the cube will increase by
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Single equivalent increase for 10% and 10%
= 10 + 10 + 10 × 10 % = 21% 100
Again, single equivalent increase for 21% and 10%= 21 + 10 + 21 × 10 % 100
= 31 + 2.1 = 33.1%
Aliter : Using Rule 14,
Increase % in volume= 3 × 10 + 3 × 102 + 102 % 100 (100)2 = 30 + 3 + 1 % = 33.1% 100
Note : Volume of cube = (Edge)3Hence, formula x + y + xy % should be used twice. 100 Correct Option: C
Single equivalent increase for 10% and 10%
= 10 + 10 + 10 × 10 % = 21% 100
Again, single equivalent increase for 21% and 10%= 21 + 10 + 21 × 10 % 100
= 31 + 2.1 = 33.1%
Aliter : Using Rule 14,
Increase % in volume= 3 × 10 + 3 × 102 + 102 % 100 (100)2 = 30 + 3 + 1 % = 33.1% 100
Note : Volume of cube = (Edge)3Hence, formula x + y + xy % should be used twice. 100
- The strength of a school increases and decreases in every alternate year by 10%. It started with increase in 2000. Then the strength of the school in 2003 as compared to that in 2000 was
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Using Rule 4,
Increase in first year = 10%
Decrease in 2nd year = 10%
Effective result= 10 - 10 - 10 × 10 % = –1% 100
Increase in 3rd year = 10%
∴ Effective result= 10 - 1 - 10 × 1 % 100
= (9 – 0.1)% = 8.9% (increase)Correct Option: A
Using Rule 4,
Increase in first year = 10%
Decrease in 2nd year = 10%
Effective result= 10 - 10 - 10 × 10 % = –1% 100
Increase in 3rd year = 10%
∴ Effective result= 10 - 1 - 10 × 1 % 100
= (9 – 0.1)% = 8.9% (increase)
