Practice Discount - quantitative aptitude Online Quiz (set-2) For All Competitive Exams

Q-1)   The marked price of a radio is Rs.4,800. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain per cent will be

(a)

(b)

(c)

(d)

Explanation:

Let CP of radio be Rs.x.

According to the question,

${108x}/100 = 4800 × 90/100 = 4320$

$x {4320 × 100}/108$ = Rs.4000

If no discount is allowed,

Gain per cent

= $800/4000 × 100 = 20%$

Using Rule 6,

M.P. = Rs.4800, D = 10%, r = 8%

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$4800/\text"CP" = {100 + 8}/{100 - 10}$

C.P. = ${4800 × 90}/108$

C.P. = 4000

Gain % (without discount)

= ${4800 - 4000}/4000 × 100$

= $800/4000 × 100$ = 20%


Q-2)   The marked price of an electric iron is Rs.690. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain per cent would be

(a)

(b)

(c)

(d)

Explanation:

Marked price = Rs.690

Discount = 10%

SP = ${690 × 90}/100$ = Rs.621

Profit = 8%

CP = $621/108 × 100$ = Rs.575

Profit without discount

= 690 - 575 = Rs.115

Profit per cent

= $115/575 × 100$ = 20%

Using Rule 9,
The marked price of an article is fixed in such a way that after allowing a discount of r% a profit of R% is obtained. Then the marked price of the article is $({r + R}/{100 - r} × 100)$% more than its cost price.

Here, r = 10% R = 20%

Required percentage

= ${r + R}/{100 - r} × 100$%

= ${10 + 20}/{100 - 10} × 100$%

= $30/90 × 100% = 33{1}/3%$

Gain % = $\text"S.P. - C.P."/\text"C.P." × 100$

(without discount)

= ${480 - 400}/400 × 100$

= $80/400 × 100$ = 20%

Using Rule 6,
If r% of profit or loss occur after giving D% discount on marked price, then
$\text"MP"/\text"CP" = {100 ± r}/{100 - D}$
(positive sign for profit and negative for loss)

Here, M.P. = Rs.690, D = 10%, r = 8%

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$600/\text"CP" = {100 + 8}/{100 - 10}$

C.P. = ${690 × 90}/108$

C.P. = Rs.575

Gain % (without discount)

= ${690 - 575}/575 = 100%$

= $115/575 × 100%$ = 20%


Q-3)   How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20% ?

(a)

(b)

(c)

(d)

Explanation:

Let C.P.of article = Rs.100

If the marked price of article be x, then

$x × 75/100$ = 120

$x = {120 × 100}/75$ = 160

i.e. 60% above the cost price

Using Rule 9,

r = 25%, R = 20%

Required percentage

= $({r + R}/{100 - r} × 100)$%

= $({25 + 20}/{100 - 25} × 100)$%

= $45/75 × 100$ = 60%


Q-4)   An article of cost price Rs.8,000 is marked at Rs.11,200. After allowing a discount of x% a profit of 12% is made. The value of x is

(a)

(b)

(c)

(d)

Explanation:

S.P. for a profit of 12%

= ${8000 × 112}/100$ = Rs.8960

Discount = 11200 - 8960 = Rs.2240

If the discount per cent be x, then

${11200 × x}/100 = 2240$

$x = {2240 × 100}/11200 = 20%$

Using Rule 6,

Here, M.P. = Rs.11200, C.P. = Rs.8000

r =12% D = x%

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$11200/8000 = {100 + 12}/{100 - x}$

= $11200/8000 = 112/{100 - x}$

100 - x = 80 ⇒ x = 20%


Q-5)   A trader wishes to gain 20% after allowing 10% discount on the marked price to his customers. At what per cent higher than the cost price must he marks his goods ?

(a)

(b)

(c)

(d)

Explanation:

Let the CP be Rs.100.

Then SP = Rs.120

Let the marked price be x.

Then, 90% of x = Rs.120

$x = {120 × 100}/90$

= $400/3 = 133{1}/3$

It is $33{1}/3$% higher than the CP.


Q-6)   The marked price of a T.V. is Rs.16,000. After two successive discounts it is sold for Rs.11,400. If the first discount is 5%, then the rate of second discount is

(a)

(b)

(c)

(d)

Explanation:

After a discount of 5%

SP = ${95 × 16000}/100$ = Rs.15200

Let the second discount be x%.

x% of 15200 = (15200 - 11400)

${x × 15200}/100 = 3800$

$x = {3800 × 100}/15200 = 25$

Second discount = 25%

Using Rule 3,

Here, M.P. = 16000, S.P. = 11400, $D_1 = 5%, D_2$ = ?

S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$

11400 = 16000$({100 - 5}/100)({100 - D_2}/100)$

$114000/{16 × 95} = 100 - D_2$

$75 = 100 - D_2 ⇒ D_2$ = 25%


Q-7)   The list price of a clock is Rs.160. A customer buys it for Rs.122.40 after two successive discounts. If first discount is 10%, the second is

(a)

(b)

(c)

(d)

Explanation:

Marked price = Rs.160

After 10% discount

S.P = $90/100 × 160$ = Rs.144

Let other discount = x%

${(100 - x)}/100 × 144$ = Rs.122.40

100 - x = $12240/144$

100 - x = 85

x = 100 - 85 = 15%

Using Rule 3,

S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$

122.40 = 160$({100 - 10}/100)({100 - D_2}/100)$

${1224000}/160 = 90 × ({100 - D_2}/1)$

$1224000/{160 × 90} = 100 - D_2$

$85 = 100 - D_2 ⇒ D_2$ = 15%


Q-8)   Successive discounts of 10%, 20% and 30% is equivalent to a single discount of

(a)

(b)

(c)

(d)

Explanation:

Using Rule 5,

Single equivalent discount for successive discounts of 10% and 20%.

= $(10 + 20 - {20 × 100}/100)$% = 28%

Single equivalent discount for 28% and 30%.

= $(28 + 30 - {28 × 30}/100)$% = 49.6%


Q-9)   Successive discounts of 10% and 20% are equivalent to a single discount of :

(a)

(b)

(c)

(d)

Explanation:

Using Rule 5,

Successive discounts of x% and y%

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

Required discount

= $(20 + 10 - {20 × 10}/100)$%

= 30 - 2 = 28%


Q-10)   A single discount equivalent to the successive discounts of 10%, 20% and 25% is

(a)

(b)

(c)

(d)

Explanation:

Single of discount for successive discounts 10% and 20%

= $(20 + 10 - {20 × 10}/100)$% = 28%

Equivalent discount for discounts 28% and 25%

= $(28 + 25 - {28 × 25}/100)$%

= 53 - 7 = 46%

Using Rule 4,
If $D_1, D_2, D_3$ are successive discounts, then equivalent discount/overall discount is (in percentage)
100 - $[({100 - D_1}/100)({100 - D_2}/100)({100 - D_3}/100) × 100]$

Single equivalent discount

= 100 - $[({100 - D_1}/100)({100 - D_2}/100)({100 - D_3}/100) × 100]$

= 100 - $[({100 - 10}/100)({100 - 20}/100)({100 - 25}/100) × 100]$

= $100 - 90/100 × 80/100 × 75/100 × 100$

= 100 - 54 = 46%


Q-11)   The marked price of an article is Rs.200. A discount of 12$1/2$%is allowed on the marked price and a profit of 25% is made. The cost price of the article is :

(a)

(b)

(c)

(d)

Explanation:

Discount = $12{1}/2% = 25/2$%

After discount S.P.

= Rs.200 × 87.5 = Rs.175

Gain % = 25%

Required C.P.

= Rs.$100/125$ × 175 = Rs.140

Using Rule 6,

Here, r = 25%, D = 12.5%,M.P. = Rs.200, C.P. = ?

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$200/\text"CP" = {100 + 25}/{100 - 12.5}$

C.P. = ${200 × 87.5}/125$ ⇒ C.P.= Rs.140


Q-12)   A shopkeeper offers 10% discount on the marked price of his articles and still makes a profit of 20%. What is the actual cost of the article marked Rs.500 for him ?

(a)

(b)

(c)

(d)

Explanation:

Let the cost price of article be x

$500 × 90/100 = 120/100 × x$

450 = ${6x}/5$

$x = {450 × 5}/6$ = Rs.375

Using Rule 6,

C.P. = ? , M.P. = Rs.500, r = 20%, D = 10%

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$500/\text"CP" = {100 + 20}/{100 - 10}$

C.P.= ${500 × 90}/120$ = Rs.375


Q-13)   A shopkeeper marks his goods 40% above the cost price. He allows a discount of 5% for cash payment to his customers. He receives Rs.1064 after paying the discount. His profit is

(a)

(b)

(c)

(d)

Explanation:

Cost price of article = Rs.x

$x × 140/100 × 95/100 = 1064$

$x = {1064 × 100 × 100}/{140 × 95}$ = Rs.800


Q-14)   A dealer offers a discount of 10% on the marked price of an article and still makes a profit of 20%. If its marked price is Rs.800, then the cost price of the article is :

(a)

(b)

(c)

(d)

Explanation:

S.P. of that article

= 800 × $90/100$ = Rs.720

He still makes 20% profit

C.P. of the article

= 720 $×100/120$ = Rs.600

Using Rule 6,
If r% of profit or loss occur after giving D% discount on marked price, then
$\text"MP"/\text"CP" = {100 ± r}/{100 - D}$
(positive sign for profit and negative for loss)

Here, r = 20%, D = 10%, M.P. = Rs.800, C.P. = ?

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$800/\text"CP" = {100 + 20}/{100 - 10}$

C.P. = ${800 × 90}/120$

C.P. = Rs.600


Q-15)   Marked price of an article is Rs.275. Shopkeeper allows a discount of 5% and he gets a profit of 4.5%. The actual cost of the article is

(a)

(b)

(c)

(d)

Explanation:

Let C.P. of article be x

${x × 104.5}/100 = {275 × 95}/100$

x × 104.5 = 275 × 95

$x = {275 × 95}/{104.5}$ = Rs.250

Using Rule 6,

M.P. = Rs.275, D = 5%,

r = 4.5%, C.P. = ?

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$275/\text"C.P." = {100 + 4.5}/{100 - 5}$

C.P. = ${275 × 95}/{104.5}$

C.P. = Rs.250


Q-16)   The difference between a discount of 40% on Rs.500 and two successive discounts of 36% and 4% on the same amount is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 5,

Single equivalent discount of two successive discounts of 36% and 4%

= 36 + 4 - ${36 × 4}/100$

= 40 - 1.44 = 38.56

Percentage difference

= 40 - 38.56 = 1.44

Required difference

= 500 × ${1.44}/100$ = Rs.7.20


Q-17)   When a shopkeeper gives 10% discount on the list price of a toy, his gain is 20%. If he had given a discount of 20%, his percentage of gain would have been

(a)

(b)

(c)

(d)

Explanation:

Let the cost price of toy be Rs.100 and the marked price be x.

${x × 90}/100 = 120$

$x = {120 × 100}/90$ = Rs.$400/3$

S.P. after a discount of 20%

= 80% of $400/3$

= ${400 × 80}/300 = 320/3 = 106{2}/3$

Profit percent

=$106{2}/3 - 100 = 6{2}/3$%


Q-18)   An article is sold at a discount of 20% and an additional discount of 30% is allowed on cash payment. If Vidya purchased the article by paying Rs.2240 in cash, the marked price of the article was

(a)

(b)

(c)

(d)

Explanation:

Let the marked price of the article be x.

Equivalent discount for successive discounts of 30% and 20%

= $(30 + 20 - {30 × 20}/100)$%

= (50 - 6)% = 44%

(100 - 44)% of x = 2240

${x × 56}/100 = 2240$

$x = {2240 × 100}/56$ = Rs.4000


Q-19)   A trader gains 15% after selling an item at 10% discount on the printed price. The ratio of the cost price and printed price of the item is

(a)

(b)

(c)

(d)

Explanation:

Let the CP of article be x and its marked price be y.

According to the question,

90% of y = 115% of x

${y × 90}/100 = {x × 115}/100$

$x/y =90/115 = 18/23$ ⇒ 18 : 23

Using Rule 6,

Here, r = 15%, D = 10%

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

= ${100 + 15}/{100 - 10}$

$\text"M.P."/ \text"C.P."= 115/90$

$\text"C.P."/ \text"M.P."= 90/115$

$\text"C.P."/ \text"M.P."= 18/23$

C.P. : M.P. = 18 : 23


Q-20)   A shopkeeper sells his goods at 10% discount on the marked price. What price should he mark on an article that costs him Rs.900 to gain 10% ?

(a)

(b)

(c)

(d)

Explanation:

C.P. = Rs.900, Gain = 10%

S.P. = Rs.$(110/100 × 900)$ = Rs.990

Let the marked price be x.

$90/100 x$ = 990

$x = {990 × 100}/90$ = Rs.1100

Using Rule 6,

Here, D = 10%, C.P. = Rs.900,

R = 10%, M.P. = ?

$\text"MP"/\text"CP" = {100 + r}/{100 - D}$

$\text"MP"/900 = {100 + 10}/{100 - 10}$

M.P. = $110/90 × 900$ = Rs.1100