# Model 2 Net Increase Or Decrease In % Practice Questions Answers Test With Solutions & More Shortcuts

#### PERCENTAGE PRACTICE TEST [11 - EXERCISES]

Question : 1

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 ?

a) 19\$11/31\$%

b) 44%

c) 40%

d) 30\$5/9\$%

Let the number be 100.

After 20% increase, number = 120

After 20% increase of 120, number

=\$120 × 120/100\$ = 144

Per cent decrease = \$44/144 × 100\$

= \$275/9 = 30{5}/9%\$

Using Rule 7 and Rule 8,

Increase % = \$(20 + 20 + {20 × 20}/100)% = 44%\$

Required % = \$(44/{100 + 44}) × 100%\$

= \$4400/144%\$

=\$275/9% = 30{5}/9%\$

Question : 2 [SSC CGL Tier-I 2016]

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%

Effective percentage decrease

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

= \$(-10 - 20 + {(-10) × (-20)}/100)%\$

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

Question : 3

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

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 : 4 [SSC CGL Tier-I 2014]

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%

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 [SSC CGL Prelim 2007]

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%

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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