model 7 sold at loss Practice Questions Answers Test with Solutions & More Shortcuts

Question : 21 [SSC CAPFs (CPO) SI 2016]

A shopkeeper purchases two items for Rs.520. One of them is sold gaining 16% and the other at a loss of 10%, thus making no profit or loss. What is the selling price of the item sold at loss?

a) Rs.288

b) Rs.200

c) Rs.232

d) Rs.320

Answer: (a)

C.P. of article sold at loss = Rs.x.

C.P. of article sold at profit = Rs.(520 - x)

According to the question,

x × $10/100 = (520 - x) × 16/100$

5x = 520 × 8 - 8x

13x = 520 × 8

$x = {520 × 8}/13$ = Rs. 320

∴ Its S.P. = ${320 × 90}/100$ = Rs.288

Question : 22 [SSC CGL Tier-II 2015]

There would be a 10% loss, if rice is sold at Rs.54 per kg. To earn a profit of 20%, the price of rice per kg will be

a) Rs.65

b) Rs.72

c) Rs.70

d) Rs.63

Answer: (b)

C.P. of rice per kg

${54 × 100}/90$ = Rs. 60

For 20% profit,

S.P. per kg. = ${60 × 120}/100$ = Rs. 72

Using Rule 3,
If an object is sold on r% Profit.

then,S.P. = C.P$[{100 + \text"Profit%"}/100]$
or
C.P. = S.P$[100/{100 + \text"Profit%"}]$

Similarly, If an object is sold on r% loss, then

S.P. = C.P.$[{100 - \text"Loss%"}/100]$
or
C.P. = S.P$[100/{100 - \text"Loss%"}]$

C.P. = S.P$[100/{100 - \text"Loss%"}]$

= $54(100/{100 - 10})$

C.P. = Rs.60

New S.P. = C.P$[{100 + \text"Profit%"}/100]$

= $60 × ({100 + 20}/100)$ = Rs.72

Question : 23 [SSC MTS 2013]

A businessman bought an article and sold it at a loss of 5%. If he had bought it for 10% less and sold it for Rs.33 more, he would have had a profit of 30%. The cost price of the article is

a) Rs.330

b) Rs.300

c) Rs.155

d) Rs.150

Answer: (d)

C.P. of the article be Rs.x

First S.P. = ${19x}/20$; C.P. = ${9x}/10$

${19x}/20 + 33$

${9x × 130}/1000 = 117/100x$

${117x}/100 - {19x}/20$ = 33

${117x - 95x}/100 = 33$

22x = 33 × 100

$x = {33 × 100}/22$ = Rs.150

Question : 24 [SSC CHSL 2015]

By selling 12 kg of potatoes for Rs.63, a shopkeeper gains 5%. What does he gain or lose percent by selling 50 kg of the same potatoes for Rs.247.50?

a) 1% loss

b) 1% profit

c) No profit, no loss

d) 2.5% loss

Answer: (a)

C.P. of 12 kg of potatoes

= Rs.$({63 × 100}/105)$ = Rs.60

C.P. of 50 kg of potatoes

= $60/12$ × 50 = Rs.250

Loss = Rs.(250 - 247.50) = Rs.2.5

Loss percent = ${2.5}/250 × 100$ = 1%

Question : 25 [SSC CGL Tier-II 2015]

A sells a cycle to B at a profit of 20% and B sells it to C at a loss of 25%. If C bought the cycle for Rs.P, then the cost price of it for A was

a) Rs.$1/20$P

b) Rs.$10/9$P

c) Rs.$9/10$P

d) Rs.$9/20$P

Answer: (b)

C.P. for A = Rs. x (let)

According to the question,

${x × 120}/100 × 75/100$ = P

$x = {P × 100 × 100}/{120 × 75}$ = Rs.$10/9$

Using Rule 15,

Here, $ r_1 = 20%, r_2$ = 25% (Loss)

C.P. for C = C.P. for A

$({1 + r_1}/100)({1 - r_2}/100)$

P = C.P. for A

$(1 + 20/100)(1 - 25/100)$

C.P. for A = ${P × 100 × 100}/{120 × 75} = {10P}/9$

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