model 1 profit x after discount y Practice Questions Answers Test with Solutions & More Shortcuts
discount PRACTICE TEST [4 - EXERCISES]
model 1 profit x after discount y
model 2 hiking & discounting
model 3 successive discount
model 4 mixed discount problems of marked price
Question : 1
A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. His gain percent is
a) 1%
b) 2%
c) 5%
d) 4%
Answer »Answer: (b)
If the C.P. of goods be Rs.100, then
Marked price = Rs.120
S.P. = ${120 × 85}/100$ = Rs.102
Hence, Profit per cent = 2%
Using Rule 8,A tradesman marks his goods r% above his cost price. If he allows his customers a discount of $r_1$% on the marked price. Then is profit or loss per cent is${r × (100 - r_1)}/100 - r_1$(Positive sign signifies profit and negative sign signifies loss).
Here, r = 20%, r1 = 15%
Gain % = ${r × (100 - r_1)}/100 - r_1$
= ${20 × (100 - 15)}/100 - 15$
= ${20 × 85}/100 - 15$
= 17 - 15 = 2%
Question : 2 [SSC DEO 2009]
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) 25%
b) 22%
c) 18%
d) 20%
Answer »Answer: (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%
Question : 3 [SSC CPO S.I.2003]
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) 28%
b) 25%
c) 20%
d) 24%
Answer »Answer: (c)
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%
Question : 4 [SSC CGL Tier-I 2013]
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) 55%
b) 60%
c) 70%
d) 50%
Answer »Answer: (b)
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%
Question : 5
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) 23%
b) 22%
c) 21%
d) 20%
Answer »Answer: (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%
IMPORTANT quantitative aptitude EXERCISES
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