Percentage
- The price of an article is first decreased by 20% and then increased by 30%. If the resulting price is 416, the original price of the article is
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If the original price of article be ₹ x, then
x × 80 × 130 = 416 100 100 ⇒ x = 416 × 100 × 100 = ₹400 80 × 130
Aliter : Using Rule 5,
Let the number be x
The number increases by= 
-20 + 30 - 20 × 30 
% = 4% 100 ⇒ x + 4x = 416 100 104x = 416 100
x = 400Correct Option: C
If the original price of article be ₹ x, then
x × 80 × 130 = 416 100 100 ⇒ x = 416 × 100 × 100 = ₹400 80 × 130
Aliter : Using Rule 5,
Let the number be x
The number increases by= -20 + 30 - 20 × 30 % = 4% 100 ⇒ x + 4x = 416 100 104x = 416 100
x = 400
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A number increased by 22 1 % gives 98. The number is 2
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If the number be x, then
x × 245 = 98 200 ∴ x = 98 × 200 = 80 245 Correct Option: C
If the number be x, then
x × 245 = 98 200 ∴ x = 98 × 200 = 80 245
- The price of an article is decreased by 10%. To restore its former value the new price must be increased by :
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Let the original price be ₹100
New price after 10% decrease = ₹90
In order to restore the price to its original value, it must be increased by ₹10
% increase= 10 × 100 = 100 = 11 1 % 90 9 9
Aliter : Using Rule 9,
Required %= 10 × 100 % 100 - 10 = 100 % = 11 1 % 9 9 Correct Option: D
Let the original price be ₹100
New price after 10% decrease = ₹90
In order to restore the price to its original value, it must be increased by ₹10
% increase= 10 × 100 = 100 = 11 1 % 90 9 9
Aliter : Using Rule 9,
Required %= 10 × 100 % 100 - 10 = 100 % = 11 1 % 9 9
- A number reduced by 25% becomes 225. What per cent should it be increased so that it becomes 375?
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Clearly, 75% of the number = 225
∴ Number = 225 × 100 = 300 75
Again, 125% of 300 = 375
Hence, the number should be increased by 25%Correct Option: A
Clearly, 75% of the number = 225
∴ Number = 225 × 100 = 300 75
Again, 125% of 300 = 375
Hence, the number should be increased by 25%
- A number is increased by 20% and then again by 20%. By what per cent should the increased number be reduced so as to get back the original number ?
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Let the number be 100.
After 20% increase, number = 120
After 20% increase of 120, number= 120 × 120 = 144 100
∴ Per cent decrease= 44 × 100 144 = 275 = 30 5 % 9 9
Aliter : Using Rule 7 and Rule 8,
Increase %= 20 + 20 + 20 × 20 % = 44% 100
Required %= 44 × 100% 100 + 44 = 4400 % 144 = 275 % = 30 5 % 9 9 Correct Option: A
Let the number be 100.
After 20% increase, number = 120
After 20% increase of 120, number= 120 × 120 = 144 100
∴ Per cent decrease= 44 × 100 144 = 275 = 30 5 % 9 9
Aliter : Using Rule 7 and Rule 8,
Increase %= 20 + 20 + 20 × 20 % = 44% 100
Required %= 44 × 100% 100 + 44 = 4400 % 144 = 275 % = 30 5 % 9 9
