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 : A number is increased by 20% and then it is decreased by 10%. Find the net increase or decrease per cent.

(a) 10% decrease

(b) 8% decrease

(c) 8% increase

(d) 10% increase

The correct answers to the above question in:

Answer: (c)

Using Rule 4,

Net % change

= $(A + B + {AB}/100)$%

Here, A = 20%, B = – 10%

Net % change = $20 - 10 - 200/100$

= 10 – 2= 8%

+ ve sign shows increase

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

Question : 1

The numerator of a fraction is increased by 20% and denominator is decreased by 20%. The value of the fraction becomes $4/5$. The original fraction is

a) $8/15$

b) $4/5$

c) $7/11$

d) $2/3$

Answer: (a)

Original fraction = $x/y$

= ${120/100x}/{y × 80/100} = 4/5$

= ${120x}/{80y} = 4/5$ ⇒ ${6x}/{4y} = 4/5$

= $x/y = 4/5 × 4/6 = 8/15$

Question : 2

The price of an article was decreased by 10% and again reduced by 10%. By what per cent should the price have been reduced once, in order to produce the same effect as these two successive reductions ?

a) 19%

b) 25%

c) 20%

d) 15%

Answer: (a)

Using Rule 6,

If a number is first decreased by a% and then by b%, then net decrease per cent is $(-a -b + {ab}/100)$% (–ve sign for decrease)

A single equivalent reduction to reduction series of x%, y%

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

=$(10 + 10 - {10 × 10}/100)$%

=(20 - 1) = 19%

Question : 3

The price of an edible oil is increased by 25%. To maintain the budget, Sushma reduces the consumption of this oil by 20%. The increase in expenditure due to this edible oil is:

a) 1

b) 3

c) 2

d) 0

Answer: (d)

Cost of edible oil = 100 per kg.

Consumption = 1 kg.

Again, New price = 125 per kg.

Consumption = 0.8 kg.

Expenditure = Rs.(125 × 0.8) = Rs.100

OR

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

=$(25 - 20 - {25 × 20}/100)$% = 0%

Question : 4

When the price of an article was reduced by 20% its sale increased by 80%. What was the net effect on the sale?

a) 44% decrease

b) 75% increase

c) 66% increase

d) 44% increase

Answer: (d)

Using Rule 5,

Required effect = $(80 - 20 - {80 × 20}/100)%$

=(60 – 16)% = 44%

Positive sign shows increase.

Question : 5

If each side of a cube is increased by 10% the volume of the cube will increase by

a) 10%

b) 25%

c) 33.1%

d) 30%

Answer: (c)

Single equivalent increase for 10% and 10%

= $(10 + 10 + {10 × 10}/100)$% = 21%

Again, single equivalent increase for 21% and 10%

= $(21 + 10 + {21 × 10}/100)%$

= 31 + 2.1 = 33.1%

Using Rule 14,

"If every side of cube is increased by a%, then increase % in volume"

= $(3a + {3a^2}/100 + a^3/(100)^2)$%

Increase % in volume

= $(3 × 10 + {3 × 10^2}/100 + 10^3/(100)2)%$

=$(30 + 3 + 1/10)$ = 33.1%

Note : Volume of cube = $(Edge)^3$

Hence, formula $(x + y + {xy}/100)%$ should be used twice.

Question : 6

A number is first increased by 10% and then it is further increased by 20%. The original number is increased altogether by

a) 15%

b) 36%

c) 32%

d) 30%

Answer: (c)

Using Rule 7,

Required percentage increase

= $(10 + 20 + {10 × 20}/100)%$= 32%

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