Practice Sold at loss - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

Q-1)   The profit earned by a shopkeeper by selling a bucket at a gain of 8% is Rs.28 more than when he sells it at a loss of 8%. The cost price (in Rupees) of the bucket is

(a)

(b)

(c)

(d)

Explanation:

Let the C.P. of bucket be Rs.x.

According to the question,

${108x}/100 - {92x}/100$ = 28

${16x}/100$ = 28

$x = {28 × 100}/16$ = Rs.175

Q-2)   An article is sold at a loss of 10%. Had it been sold for Rs.90 more, there would have been a gain of 5%. The original sale price of the article (in Rs.) is :

(a)

(b)

(c)

(d)

Explanation:

If the C.P. of article be Rs.x, then

${105x}/100 - {90x}/100$ = 90

${15x}/100 = 90$

$x = {90 × 100}/15$ ⇒ x = Rs.600

Original S.P. = ${600 × 90}/100$ = Rs.540

Q-3)   By selling 4 articles for 1 rupee, a man loses 4%. Had he sold three articles per rupee, the profit would have been :

(a)

(b)

(c)

(d)

Explanation:

C.P. of 1 article

= $1/4 × 100/96$ = Rs.$25/96$

C.P. of 3 articles = Rs.$75/96$

Gain = 1 - $75/96$

=${96 - 75}/96 = 21/96 = 7/32$

Gain per cent = ${7/32}/{75/96}$ × 100

= $7/32 × 96/75 × 100$ = 28%

Q-4)   Mohan sold his watch at 10% loss. If he had sold it for Rs.45 more, he would have made 5% profit. The selling price (in Rs.) of the watch was

(a)

(b)

(c)

(d)

Explanation:

If the C.P. of watch be Rs.x, then

First S.P. = ${9x}/10$

${105x}/100 - {9x}/10 = 45$

${105x - 90x}/100 = 45$

${15x}/100 = 45$

$x = {45 × 100}/15$ = Rs.300

S. P. = ${300 × 9}/10$ = Rs.270

Using Rule 11,

Here, x = 10%, R = Rs.45, y = 5%

C.P. = ${R × 100}/{y + x}$

= $4500/{10 + 5} = 4500/15$ = 300

S.P. = 300 - 300 × $10/100$

S.P. = Rs.270

Q-5)   A man sold an article at a loss of 20%. If he has sold that article for Rs.12 more he would have gained 10%. Find the cost price of that article :

(a)

(b)

(c)

(d)

Explanation:

Simple Approach

80% x + 12 = 110%

Let x be the cost price

30% x = 12 = $12/30 × 100$ = Rs.40

Using Rule 11,

Here, x = 20%, R= 12, y = 10%

C.P. = ${R × 100}/{y + x}$

= ${12 × 100}/{20 + 10}$ = Rs.40

Q-6)   A businessman sells a commodity at 10% profit. If he had bought it at 10% less and sold it for Rs.2 less, then he would have gained 16$2/3%$. The cost price of the commodity is

(a)

(b)

(c)

(d)

Explanation:

Let the first CP of the commodity be Rs.100.

First SP = Rs.110; Second CP = Rs.90

Gain% = $50/3%$

Second SP = $(100 + 50/3)%$ of 90

= Rs.$(90 × 350/300)$ = Rs.105

Difference of first and second S.P.

= Rs.(110–105) = Rs.5

Since, If the difference is Rs.5, the CP = Rs.100.

Since, If the difference be Rs.2, the

CP = $100/5 × 2$ = Rs.40

Q-7)   A man sells an article at 10% loss. If he had sold it at Rs.10 more, he would have gained 10%. The cost price of the article is

(a)

(b)

(c)

(d)

Explanation:

Let the C.P be Rs.x.

First selling price = 90% of x = Rs.${9x}/10$

Second selling price = $({9x}/10 + 10)$

110% of $x = ({9x}/10 + 10)$

${11x}/10 = {9x}/10 + 10 ⇒ {2x}/10 = 10$

$x = {10 × 10}/2 = 50 = Rs.50$

Using Rule 11,

Here, x = 10%, R= 10, y = 10%

C.P. = ${R × 100}/{y + x}$

= ${10 × 100}/{10 + 10}$ = Rs.50

Q-8)   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)

(b)

(c)

(d)

Explanation:

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

Q-9)   An article is sold at a loss of 10%. Had it been sold for Rs.9 more, there would have been a gain of 12$1/2$% on it. The cost price of the article is :

(a)

(b)

(c)

(d)

Explanation:

Let the cost price of the article = Rs.x

S.P. at 10% loss

= $x × 90/100 = {9x}/10$

S.P. at $12{1}/2%$ gain

=$x × {100 + 12{1}/2}/100 = {225x}/200$

According to the question

${9x}/10 + 9 = {225x}/200$

180x + 1800 = 225x

225x - 180x = 1800

45x = 1800 ⇒ x = Rs.40

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 = 10%, R= 9, y = 12.5%

C.P. = ${R × 100}/{y + x}$

= ${9 × 100}/{12.5 + 10} = 900/{22.5}$ = Rs.40

Q-10)   A book vendor sold a book at a loss of 20%. Had he sold it for Rs.108 more, he would have earned a profit of 30%. Find the cost price of the book ?

(a)

(b)

(c)

(d)

Explanation:

If the cost price of the book be Rs.x, then

${x × 80}/100 + 108 = {x × 130}/100$

${5x}/10 = 108 ⇒ x = Rs.216$

Using Rule 11

Here, x = 20%, R= Rs.108, y=30%

C.P. = ${R × 100}/{y + x}$

= ${108 × 100}/{30 + 20}$

= $10800/50$ = Rs.216