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 : 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

The correct answers to the above question in:

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

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

Question : 1

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 : 2

If the numerator of a fraction is increased by 20% and the denominator is decreased by 5%, the value of the new fraction becomes $5/2$. The original fraction is

a) $3/18$

b) $48/95$

c) $95/48$

d) $24/19$

Answer: (c)

Let original fraction be $x/y$

According to the question,

${120/100x}/{{95y}/100} = 5/2$

${120x}/{95y} = 5/2$

$x/y = 5/2 × 95/120 = 95/48$

Question : 3

The price of an article is reduced by 25% but the daily sale of the article is increased by 30%. The net effect on the daily sale receipts is

a) 2$1/2$% decrease

b) 2% decrease

c) 2% increase

d) 2$1/2$% increase

Answer: (a)

Let the price of the article be Rs.100 and the daily sale be 100 units.

Revenue day = 100 × 100 = Rs.10000

New receipts = 75 × 130 = Rs.9750

Decrease = Rs.(10000 – 9750) = Rs.250

% decrease = $250/10000 × 100 = 2{1}/2%$

Using Rule 5,

If a number is decreased by a% and then it is increased by b%, then net increase or decrease per cent is $(-a + b - {ab}/100)$% (Negative sign for decrease; Positive sign for increase)

Required change = $(a - b - {ab}/100)$

= $(30 - 25 – {30 × 25}/100)%$

= $(5 - 15/2) = –2.5% = 2{1}/2%$ decrease.

Question : 4

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 : 5

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%

Answer: (a)

Using Rule 7,

Effective percentage increase

= $(20 + 20 + {20 × 20}/100)%$= 44%

Question : 6

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 %

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