model 2 hiking & discounting Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 4 EXERCISES
The following question based on discount topic of quantitative aptitude
(a) 10%
(b) 20%
(c) 16%
(d) 8%
The correct answers to the above question in:
Answer: (c)
Let the cost price be x
Mark Price
= $(1 + 20/100)x = 1.2x$
Cash price = $(1 - 30/100)1.2x$
= 0.7 × 1.2x = 0.84x
Net Loss = x - 0.84x = 0.16x
Net loss% = ${0.16x}/x × 100$ = 16%
Using Rule 8,
Here, r = 20%, $r_1$ = 30%
Profit or loss
= ${r × (100 - r_1)}/100 - r_1$
= ${20 × (100 - 30)}/100 - 30$
= 14 - 30 = –16% = 16% loss
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Question : 1
Maha Bazaar offers 20% discount on bags which have been marked 50% above the cost price. Amarnath pays Rs.840 for a bag. Then the cost price of the bag is
a) Rs.700
b) Rs.810
c) Rs.790
d) Rs.672
Answer »Answer: (a)
Let the cost price be Rs.100.
Marked price = Rs.150
S.P. = ${150 × 80}/100$ = Rs.120
when S.P. = 120, C.P. = Rs.100
when S.P. = 840
C.P.= $100/120 × 840$ = Rs.700
Using Rule 8,
Here, r = 50%, $r_1$ = 20%, S.P. = Rs.840
Gain % = ${r × (100 - r_1)}/100 - r_1$
= ${50 × (100 - 20)}/100 - 20$
= ${50 × 80}/100 - 20$= 20%
We know that
Gain % = $\text"S.P. - C.P."/{C.P.} ×100$
20 = $({840 - x}/x) × 100$
20x= 84000 - 100x
120x = 84000
x = 700
∴ C.P. = Rs.700
Question : 2
A dealer marks his goods 20% above their cost price. He then allows some discount on marked price so that he makes a profit of 10%. The rate of discount is
a) 9$1/3$%
b) 8$1/3$%
c) 8$2/3$%
d) 10$1/3$%
Answer »Answer: (b)
Let cost price of article = Rs.100
Marked price of article
= ${100 × 120}/100$ = Rs.120
S.P. of article = Rs.110
Discount = 120 - 110 = Rs.10
If discount = x%, then
${120 × x}/100$ = 10
$x = {10 × 100}/120 = 25/3 = 8{1}/3$%
Using Rule 8,
Here, r = 20%, Profit = 10%
Let, discount $r_1$ = x%
Profit % = ${r × (100 - r_1)}/100 - r_1$
10 = ${20 × (100 - x)}/100 - r_1$
1000 = 2000 - 20x - 100x
–1000 = –120x
$x = 100/12 = 25/3 = 8{1}/3$%
Question : 3
The marked price is 20% higher than cost price. A discount of 20% is given on the marked price. By this type of sale, there is
a) 2% loss
b) 4% gain
c) no loss no gain
d) 4% loss
Answer »Answer: (d)
Let Cost price = Rs.100
Marked price = Rs.120
Selling price = ${120 × 80}/100$ = Rs.96
Loss = Rs.4 and loss per cent = 4%
Using Rule 8,
Here, r = 20%, $r_1$ = 20%
Loss % = ${r × (100 - r_1)}/100 - r_1$
= ${20 × (100 - 20)}/100 - 20$
= ${20 × 80}/100 - 20$
= –4% (–ve sign shows loss)
= 4% loss
Question : 4
A tradesman marks his goods at 25% above its cost price and allows purchasers a discount of 12$1/2$% for cash payment. The profit, he thus makes, is
a) 9$1/2$%
b) 8$3/8$%
c) 8$1/2$%
d) 9$3/8$%
Answer »Answer: (d)
Let the cost price of article = Rs.100
Marked price = Rs.125
SP of the article
= $(100 - 25/2)$% of 125
= $175/2$% of 125
= ${125 × 175}/{2 × 100} = 875/8$
= Rs.109$3/8$
Gain percent
= $(109{3/8} -100) = 9{3}/8$%
Using Rule 8,
Here, r = 25%, $r_1 = 12{1}/2$% = 12.5%
Profit % = ${r × (100 - r_1)}/100 - r_1$
= ${25 × (100 - {12.5})}/100 - {12.5}$
= ${25 × 87.5}/100 - 12.5$
= 21.875 - 12.5
= 9.375 = 9$3/8$%
Question : 5
A dealer marks his goods at 25% above the cost price and allows a discount of 10% for cash payment. His profit % is :
a) 15%
b) 20%
c) 12.5%
d) 17.5%
Answer »Answer: (c)
Let Cost price of article = Rs.100
Marked price = Rs.125
S.P. = ${125 × 90}/100$ = Rs.112.5
Gain = 112.5 - 100 = 12.5
Gain percent = 12.5%
Using Rule 8,
Here, r = 25%, $r_1$ = 10%
Profit % = ${r × (100 - r_1)}/100 - r_1$
= ${25 × (100 - 10)}/100 - 10$
= ${25 × 90}/100 - 10$
= 22.5 - 10 = 12.5%
Question : 6
To gain 8% after allowing a discount of 10%, by what per cent cost price should be hiked in the list price ?
a) 11%
b) 20%
c) 18%
d) 9%
Answer »Answer: (b)
Let the cost price be Rs.100
and marked price be x.
${x × 90}/100 = 108$
${9x}/10 = 108$
$x = {108 × 10}/9 = 120$
Required Percent = 20%
Using Rule 8,
Here, Gain % = 8%, $r_1$ = 10%, r = ?
Gain % = ${r × (100 - r_1)}/100 - r_1$
8 = ${r × (100 - 10)}/100 - 10$
8 = ${r × 90}/100 - 10$
8 = ${r × 9}/10$ = 20%
GET discount PRACTICE TEST EXERCISES
model 1 profit x after discount y
model 2 hiking & discounting
model 3 successive discount
model 4 mixed discount problems of marked price
discount Shortcuts and Techniques with Examples
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