model 1 profit x after discount y Practice Questions Answers Test with Solutions & More Shortcuts

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: (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: (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: (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: (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: (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%

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