model 2 net increase or decrease in % Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on percentage topic of quantitative aptitude

Questions : If a number is increased by 20% and the resulting number is again increased by 20%, what per cent is the total increase ?

(a) 44%

(b) 40%

(c) 41%

(d) 48%

The correct answers to the above question in:

Answer: (a)

Using Rule 7,

Effective percentage increase

= $(20 + 20 + {20 × 20}/100)%$= 44%

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Read more net increase or decrease Based Quantitative Aptitude Questions and Answers

Question : 1

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

a) 400

b) 600

c) 500

d) 200

Answer: (c)

Effective percentage = $(-20 + 20 - {20 × 20}/100)$= - 4%

If the number be x, then 4% of x = 20

$x × 4/100 = 20$

$x = {20 × 100}/4 = 500$

Using Rule 3,

If an amount is increased by a% and then it is reduced by a% again, then percentage change will be a decrease of $a^2/100%$

Let the number be x

Decrease % = $20^2/100$ = 4%

x – 4% of x = x – 20

${4x}/100 = + 20 ⇒ x = 500$

Question : 2

The sum of two numbers is 520. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is

a) 210

b) 300

c) 240

d) 280

Answer: (c)

Larger number = x and smaller number = 520 – x

${96x}/100 = {520 - x}/100 × 112$

96x = 520 × 112 – 112x

112x + 96x = 520 × 112

208x = 520 × 112

$x = {520 × 112}/208 = 280$

Smaller number = 520 – 280 = 240

Question : 3

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

a) decreased by 8.9%

b) decreased by 9.8%

c) increased by 9.8%

d) increased by 8.9%

Answer: (d)

Using Rule 4,

If a number is increased by a% and then it is decreased by b%, then the resultant change in percentage will be $(a - b - {ab}/100)$% (Negative for decrease, Positive for increase)

Increase in first year = 10%

Decrease in 2nd year = 10%

Effective result = $(10 - 10 - {10 × 10}/100)% = -1%$

Increase in 3rd year = 10%

Effective result = $(10 - 1 - {10 × 1}/100)$%

= (9 – 0.1)% = 8.9% (increase)

Question : 4

Two successive price increases of 10% and 10% of an article are equivalent to a single price increase of

a) 20%

b) 22%

c) 21%

d) 19%

Answer: (c)

Using Rule 7,

If a number is first increased by a% and then again increased by b%, then total increase per cent is $(a + b + {ab}/100)$%

Tricky approach

Single equivalent percentage increase in price

= $(10 + 10 + {10 × 10}/100)%$ = 21 %

Question : 5

If price of a book is first decreased by 25% and then increased by 20%, the net change in the price of the book will be

a) 5% decrease

b) 5% increase

c) no change

d) 10% decrease

Answer: (d)

The net change in price

= $(-25 +20 - {25 × 20}/100)$

= (–25 + 20 – 5)% = – 10%

Negative sign shows decrease.

Question : 6

A number is increased by 10% and then it is decreased by 10%. The net change in the number is

a) 2% decrease

b) 1% decrease

c) 1% increase

d) no increase or decrease

Answer: (b)

Using Rule 4,

Net change

= $(10 - 10 - {10 × 10}/100)%$

= –1% = 1% decrease

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