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 the income tax is increased by 19%, the net income is reduced by 1%. The rate of income tax is

(a) 4%

(b) 7.2%

(c) 5%

(d) 6%

The correct answers to the above question in:

Answer: (c)

Let the income be Rs.x and the rate of income tax be y %

According to the question,

${xy × 1.19}/100 - {xy}/100 = (x - {xy}/100) × 1/100$

$1.19 xy - xy = x - {xy}/100$

$0.19 y = 1 - y/100$

$y/100 + 0.19y = 1 ⇒ ({1 + 19}/100) = 1$

$y = 100/20 = 5%$

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

Question : 1

If a number is increased by 25% and the resulting number is decreased by 25%. then the percentage increase or decrease finally is

a) decreased by $6{1}/4$%

b) increased by 6%

c) increased by $6{1}/4$%

d) no change

Answer: (a)

Using Rule 4,

Effective value = $(x + y +{xy}/100)$%

= $(25 - 25 - {25 × 25}/100)%$

[Here, x = 25, y = –25]

= –6.25% = $6{1}/4$% decreased

(Negative value shows decrease).

Question : 2

The cost of an article worth Rs.100 is increased by 10% first and again increased by 10%. The total increase in rupees is

a) 21

b) 121

c) 110

d) 20

Answer: (a)

Using Rule 7,

Percentage effect = $(10 + 10 + {10 × 10}/100)$% = 21 %

Increase = Rs.21

Question : 3

A number increased by 22$1/2$% gives 98. The number is

a) 18

b) 81

c) 80

d) 45

Answer: (c)

If the number be x, then $x × 245/200 = 98$

$x = {98 × 200}/245 = 80$

Question : 4

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

a) 30%

b) 25%

c) 50%

d) 40%

Answer: (c)

Man's income = Rs.100 (let)

Expenditure = Rs.75

Savings = Rs.25

New income = ${100 × 120}/100 = Rs.120$

New expenditure = ${75 × 110}/100 = Rs.82.5$

Savings = 120 – 82.5 = Rs.37.5

Increase in savings = 37.5 – 25 = Rs.12.5

Increase per cent = $12.5/25 × 100 = 50%$

Question : 5

Salary of a person is first increased by 20%, then it is decreased by 20%. Percentage change in his salary is :

a) 4% increased

b) 20% increased

c) 8% decreased

d) 4% decreased

Answer: (d)

Using Rule 4,

"If a number is increased by a% and then it is decreased by b%, then resultant change in percentage will be"

$(a - b - {ab}/100)$%

Change in his salary = $(20 - 20 - {20 × 20}/100)$%

= $(- 400/100)% = - 4%$

i.e. 4% decrease

Note : If A is first increased by x% and then decreased by y% the net % change

= $(x - y - {xy}/100)$%

If the result is positive, the change indicates an increase and if the result is negative, the change indicates a decrease.

Question : 6

A number is decreased by 10% and the resulting number is again decreased by 20%. What is the final percentage of decrease?

a) 26%

b) 28%

c) 27%

d) 25%

Answer: (b)

Effective percentage decrease

= $(x + y + {xy}/100)%$

= $(-10 - 20 + {(-10) × (-20)}/100)%$

= (-30 + 2)% = -28%

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