Percentage
- 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
-
View Hint View Answer Discuss in Forum
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 the income tax is increased by 19%, the net income is reduced by 1%. The rate of income tax is
-
View Hint View Answer Discuss in Forum
Let the income be ₹x and the rate of income tax be y %
According to the question,xy × 1.19 - xy 100 100 = 
x - xy 
× 1 100 100 ⇒ 1.19 xy – xy = x - xy 100 ⇒ 1.19y = 1 - y 100 ⇒ y + 1.19y = 1 100 ⇒ y 1 + 19 = 1 100 ⇒ y = 100 = 5% 20 Correct Option: C
Let the income be ₹x and the rate of income tax be y %
According to the question,xy × 1.19 - xy 100 100 = x - xy × 1 100 100 ⇒ 1.19 xy – xy = x - xy 100 ⇒ 1.19y = 1 - y 100 ⇒ y + 1.19y = 1 100 ⇒ y 1 + 19 = 1 100 ⇒ y = 100 = 5% 20
- A number is first decreased by 10% and then increased by 10%. The number so obtained is 50 less than the original number. The original number is
-
View Hint View Answer Discuss in Forum
Let original number be x.
∴ 90 x × 110 = x - 50 100 100 ⇒ 99x = x - 50 100 ⇒ x - 99x = 50 100 ⇒ x = 50 100
⇒ x = 5000
Aliter : Using Rule 3,
Let the number be xDecrease % = 102 % = 1% 100
⇒ x – 1% of x =x – 50x = 50 ⇒ x = 5000 100 Correct Option: B
Let original number be x.
∴ 90 x × 110 = x - 50 100 100 ⇒ 99x = x - 50 100 ⇒ x - 99x = 50 100 ⇒ x = 50 100
⇒ x = 5000
Aliter : Using Rule 3,
Let the number be xDecrease % = 102 % = 1% 100
⇒ x – 1% of x =x – 50x = 50 ⇒ x = 5000 100
- The number of employees working in a farm is increased by 25% and the wages per head are decreased by 25%. If it results in x % decrease in total wages, then the value of x is
-
View Hint View Answer Discuss in Forum
Let the original number of employees be 100 and wages per head be ₹100.
Total wages = ₹(100 × 100) = ₹10000
New number of employees = 125
New wages per head = ₹75
Total new wages = ₹(125 × 75) = ₹9375
Decrease
= ₹(10000 – 9375) = ₹625
∴ Percentage decrease= 625 × 100 10000 = 625 = 25 % 100 25 Correct Option: D
Let the original number of employees be 100 and wages per head be ₹100.
Total wages = ₹(100 × 100) = ₹10000
New number of employees = 125
New wages per head = ₹75
Total new wages = ₹(125 × 75) = ₹9375
Decrease
= ₹(10000 – 9375) = ₹625
∴ Percentage decrease= 625 × 100 10000 = 625 = 25 % 100 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 ?
-
View Hint View Answer Discuss in Forum
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
