model 2 net increase or decrease in % Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

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 % = $(44/{100 + 44}) × 100%$

= $4400/144%$

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

Answer: (b)

Effective percentage decrease

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

= $(-10 - 20 + {(-10) × (-20)}/100)%$

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

Answer: (d)

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.

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 = $12.5/25 × 100 = 50%$

Answer: (c)

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

According to the question,

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

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

$0.19 y = 1 - y/100$

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

$y = 100/20 = 5%$