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

Question : 31 [SSC CGL Prelim 2004]

The number of employees working in a farm is increased by 25% and the wages per head are decreased by 25%. If it results in x % decrease in total wages, then the value of x is

a) 25%

b) $25/4$%

c) 20%

d) 0%

Answer: (b)

Let the original number of employees be 100 and wages per head be Rs.100.

Total wages = Rs.(100 × 100) = Rs.10000

New number of employees = 125

New wages per head = Rs.75

Total new wages = Rs.(125 × 75) = Rs.9375

Decrease = Rs.(10000 – 9375) = Rs.625

Percentage decrease =$625/10000 × 100$

=$625/100 = 25/4%$

Question : 32 [SSC CGL 2000]

The price of an article is decreased by 10%. To restore its former value the new price must be increased by :

a) 11%

b) 11$1/9$%

c) 9$1/11$%

d) 10%

Answer: (b)

Let the original price be Rs.100

New price after 10% decrease = Rs.90

In order to restore the price to its original value, it must be increased by Rs.10

% increase = $10/90 × 100 = 100/9 = 11{1}/9%$

Using Rule 9,

If ‘x' is A% less than ‘y', then y is more than ‘x' by Required% = $(A/{(100 - A)} × 100)%$(increase)

Required % = $10/{100 - 10} × 100%$

= $100/9% = 11{1}/9$%

Question : 33 [SSC CGL Tier-I 2013]

The price of an article is first decreased by 20% and then increased by 30%. If the resulting price is Rs.416, the original price of the article is

a) Rs.405

b) Rs.450

c) Rs.400

d) Rs.350

Answer: (c)

If the original price of article be Rs.x, then

$x × 80/100 × 130/100$ = 416

$x = {416 × 100 × 100}/{80 × 130}$= Rs.400

Using Rule 5,

Let the number be x

The number increases by

$(- 20 + 30 - {20 × 30}/100)$% = 4%

$x + {4x}/100$ = 416

${104x}/100$ = 416 ⇒ x = 400

Question : 34 [SSC CGL Tier-I 2010]

The price of an article was first increased by 10% and then again by 20%. If the last increased price be Rs.33, the original price was

a) Rs.27.50

b) Rs.25

c) Rs.26.50

d) Rs.30

Answer: (b)

Using Rule 7,

Simple Approach

Effective increase percentage

= $(10 + 20 + {20 × 10}/100)%$ = 32%

$x × 132/100 = 33$

$x = {33 × 100}/132$ = Rs.25

Question : 35 [SSC CAPFs SI 2015]

A number is increased by x %; to get back to the original number, it is to be reduced by

a) ${100x}/{100 + x}$%

b) $x/{100 + x}$%

c) ${10x}/{100 + x}$%

d) x %

Answer: (a)

Initial value → increasing value

${P × x}/100$ → increased value → P + ${Px}/100$

= $P({100 + x}/100)$

Required answer = $(x/{100 + x} × 100)%$

IMPORTANT quantitative aptitude EXERCISES

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