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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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