Percentage
- A number is increased by x %; to get back to the original number, it is to be reduced by
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Initial value increasing value P × x → increased value → P + Px 100 100 = P 100 + x 100
∴ Required answer= x × 100 % 100 + x Correct Option: B
Initial value increasing value P × x → increased value → P + Px 100 100 = P 100 + x 100
∴ Required answer= x × 100 % 100 + x
- A number is first decreased by 20%. The decreased number is then increased by 20%. The resulting number is less than the original number by 20. Then the original number is
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Effective percentage
= - 20 + 20 - 20 × 20 = – 4% 100
If the number be x, then
4% of x = 20⇒ x × 4 = 20 100 ⇒ x = 20 × 100 = 500 4
Aliter : Using Rule 3,
Let the number be xDecrease % = 202 = 20 100
x – 4% of x = x – 204x = + 20 100
x = 500Correct Option: C
Effective percentage
= - 20 + 20 - 20 × 20 = – 4% 100
If the number be x, then
4% of x = 20⇒ x × 4 = 20 100 ⇒ x = 20 × 100 = 500 4
Aliter : Using Rule 3,
Let the number be xDecrease % = 202 = 20 100
x – 4% of x = x – 204x = + 20 100
x = 500
- The difference between the value of the number increased by 20% and the value of the number decreased by 25% is 36. Find the number.
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Let the number be x.
∴ (20 + 25)% of x = 36⇒ 45x = 36 100 ⇒ x = 36 × 100 = 80 45 Correct Option: D
Let the number be x.
∴ (20 + 25)% of x = 36⇒ 45x = 36 100 ⇒ x = 36 × 100 = 80 45
- 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)
- 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