model 9 selling an article & interchanging its values Practice Questions Answers Test with Solutions & More Shortcuts

Question : 21 [SSC CGL Tier-I 2016]

The selling price of an article is $8/5$th of its cost price. Then the gain percentage is

a) 20%

b) 60%

c) 68%

d) 28%

Answer: (b)

C.P. of article = Rs.x

Its S.P. = Rs.${8x}/5$

Profit = ${8x}/5 - x$

= ${8x - 5x}/5$ = Rs.${3x}/5$

Profit per cent = ${{3x}/5}/x × 100$

= $3/5$ × 100 = 60%

Question : 22 [SSC Constable 2013]

By selling 90 ball pens for Rs.160 a person loses 20%. The number of ball pens, which should be sold for Rs.96 so as to have a profit of 20% is

a) 36

b) 46

c) 47

d) 37

Answer: (a)

Using Rule 3,

C.P. of 90 ball pens

= $100/80$ × 160 = Rs.200

S.P. for a gain of 20%

= ${200 × 120}/100$ = Rs.240

Since, Rs.240 = 90 ball pens

Rs.96 = $90/240$ × 96 = 36

Question : 23 [SSC CGL Prelim 2005]

By selling a plot of land for Rs.45,000 a person loses 10%. At what price should he sell it to gain 15%?

a) Rs.50,000

b) Rs.57,500

c) Rs.60,000

d) Rs.55,000

Answer: (b)

Using Rule 3,

C.P. = $100/{100 - Loss%}$ × S.P.

= $100/90$ × 45000 = Rs.50000

S.P. = 115% of Rs.50000

= Rs.${50000 × 115}/100$ = Rs.57,500

Question : 24 [SSC CGL Prelim 2002]

On selling an article for Rs.105 a trader loses 9%. To gain 30% he should sell the article at

a) Rs.126

b) Rs.150

c) Rs.139

d) Rs.144

Answer: (b)

Simple Approach

Let C.P. = 100x

(100 - 9)x = 105

(100 + 30)% x = $105/91$ × 130 = Rs.150

Using Rule 3,

C.P. = 105 × $(100/{100 - 9}) = {105 × 100}/91$

C.P. = $1500/13$

New S.P.= $1500/13 × ({100 + 30}/100)$ =15 × 10 = Rs.150

Question : 25 [SSC MTS 2013]

A radio dealer sold a radio at a loss of 2.5%. Had he sold it for Rs.100 more, he would have gained 7$1/2$% . In order to gain 12$1/2$% , he should sell it for

a) Rs.1080

b) Rs.850

c) Rs.925

d) Rs.1125

Answer: (d)

If C.P. of radio be Rs.x, then 10% of x = 100

x = 1000

For a gain of 12$1/2$%

S.P. = 1000 × $({100 + {25/2}})/100$

= ${1000 × 225}/200$ = Rs.1125

Using Rule 11,
A man sells his items at a profit/loss of x%.
If he had sold it for Rs. R more,
he would have gained/lost y%.
Then. C.P. of items = $R/{(y ± x)}$ × 100
'+' = When one is profit and other is loss.
'–' = When both are either profit or loss.

Here, x = 2.5%, R = 100, y = 7$1/2$%

C.P. = $R/{y + x}$ × 100

= ${100 × 100}/{2.5 + 7.5}$ = Rs.1000

Now New S.P. = C.P. × $({100 + Profit%}/100)$

= $1000({100 + 12.5}/100)$

= 10 × 112.5 = Rs.1125

IMPORTANT quantitative aptitude EXERCISES

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