Practice Discount - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. His gain percent is
(a)
(b)
(c)
(d)
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%
Q-2) A shopkeeper marks the price of an item keeping 20% profit. If he offers a discount of 12$1/2$% on the marked price, his gain percent will be
(a)
(b)
(c)
(d)
Let the cost price be Rs.100.
Marked price = Rs.120
SP = 87$1/2$% of 120
= $175/200 × 120$ = Rs.105
Gain per cent = 5%
Using Rule 8,
Here, r = 20%, $r_1 = 12{1}/2$%
Profit % = ${r × (100 - r_1)}/100 - r_1$
= ${20 × (100 - {25/2})}/100 - {25/2}$
= ${20 × 175}/200$ - 12.5
= 17.5 - 12.5 = 5%
Q-3) A dealer buys a car listed at Rs.200000 at successive discounts of 5% and 10%. If he sells the car for 179550, then his profit is
(a)
(b)
(c)
(d)
Equivalent discount
= $10 + 5 - {10 × 5}/100 = 14.5%$
CP (for buyer)
= 85.5% of Rs.200000
= Rs.$({85.5 × 200000}/100)$ = Rs.171000
SP = Rs.179550
Gain = Rs.(179550 –171000) = Rs.8550
Gain % = $8550/171000 × 100 =5%$
Using Rule 3,
Here, M.P. = 200000,
S.P. is C.P. byer for $D_1 = 5%, D_2$ = 10%
S.P.= M.P.$({100 - D_1}/100)({100 - D_2}/100)$
= 200000$({100 - 5}/100)({100 - 10}/100)$
= 20 × 95 × 90
C.P. for buyer =171000
S.P. = 179550
Profit =S.P. - $\text"C.P."/\text"C.P" ×100%$
= $8550/171000$ × 100 = 5%
Q-4) A trader marked the price of his commodity so as to include a profit of 25%. He allowed discount of 16% on the marked price. His actual profit was :
(a)
(b)
(c)
(d)
Let the C.P. be Rs.100
Marked price = Rs.125
S.P. = 8% of 125
= ${84 × 125}/100$ = Rs.105
Profit = Rs.(105 - 100) = Rs.5
Profit % = 5%
Q-5) A sells a scooter priced Rs.36,000. He gives a discount of 8% on the first Rs.20,000 and 5% on the next Rs.10,000. How much discount can he offered on the remaining Rs.6,000 if he is to get as much as when 7% discount is allowed on the total ?
(a)
(b)
(c)
(d)
Discount on Rs.36000
= ${36000 × 7}/100$ = Rs.2520
Discount on first Rs.20,000
= ${20000 × 8}/100$ = Rs.1600
Discount on next Rs.10,000
= ${10,000 × 5}/100$ = Rs.500
Discount on remaining Rs.6,000
= 2520 - (1600 + 500) = Rs.420
∴ Required percent
= ${420 × 100}/6000$ = 7%
Q-6) Two successive discounts of 20% and 20% is equivalent to a single discount of
(a)
(b)
(c)
(d)
Using Rule 5,
Equivalent single discount
= $(20 + 20 - {20 × 20}/100)$% = 36%
Q-7) An article is listed at Rs.920. A customer pays Rs.742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is
(a)
(b)
(c)
(d)
Total discount
= Rs.(920 - 742.90) = Rs.177.10
First discount = 15%
Discount = 15% of 920
= ${920 × 15}/100$ = Rs.138
Price after this discount
= 920 - 138 = Rs.782
Remaining discount
= 177.10 - 138 = Rs.39.10
Let the second discount be x %.
${782 × x}/100 = 39.10$
$x = {39.10 × 100}/782$ = 5%
Using Rule 3,
Here, M.P. = Rs.920, S.P. = Rs.742.90, $D_1 = 15%, D_2$ = ?
S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$
742.90 = 920 $({100 - 15}/100)({100 - D_2}/100)$
$7429000/{920 × 85} = 100 - D_2$
95 = 100 - $D_2 ⇒ D_2$ = 5%
Q-8) The marked price of a watch was Rs.720/-. A man bought the same for Rs.550.80, after getting two successive discounts, the first at 10%. What was the second discount rate?
(a)
(b)
(c)
(d)
Marked price = Rs.720
Actual price = Rs.550.80
First discount = 10%
Let the second discount be x%
Then, we can write
720 (1 - 0.10) (1–0.01x) = 550.80
720 × 0.9 (1– 0.01x) = 550.8
648 (1 - 0.01x) = 550.8
1 - 0.01 x= ${550.8}/648$
0.01 x = $1 - {550.8}/648$
$x = {1 - 0.85}/{0.01}$
x = 0.15 × 100 ⇒ x= 15
Second discount = 15%
Q-9) The marked price of an article is Rs.500. It is sold at successive discounts of 20% and 10%. The selling price of the article (in rupees) is :
(a)
(b)
(c)
(d)
Equivalent discount of successive discounts of 20% and 10%
= $(20 + 10 - {20 × 10}/100)$% = 28%
Selling Price = (100 - 28) % of Rs.500 = 72 % of 500
= Rs.${500 × 72}/100$ = Rs.360
Using Rule 3,When successive Discounts $D_1, D_2, D_3$, so on, are given thenSP = MP$({100 - D_1}/100)({100 - D_2}/100)({100 - D_3}/100)$
M.P. = Rs.500, $D_1 = 20%, D_2$ = 10%
S.P.= M.P.$({100 - D_1}/100)({100 - D_2}/100)$
= $500({100 - 20}/100)({100 - 10}/100)$
= $500 × 80/100 × 90/100$ = Rs.360
Q-10) The marked price of watch was Rs.820. A man bought the watch for Rs.570.72 after getting two successive discounts, of which the first was 20%. The second discount was
(a)
(b)
(c)
(d)
Total discount
=Rs.(820 - 570.72) = Rs.249.28
First discount = $820 × 20/100$ = Rs.164
Second discount
= Rs.(249.28 - 164) = Rs.85.28
Price of the article after first discount
= Rs.(820 - 164) = Rs.656
If the second discount be x% , then
x% of 656 = 85.28
$x = {85.28 × 100}/656 = 13%$
Using Rule 3,
Here, M.P. = Rs.820, S.P. = 570.72, $D_1 = 20%, D_2$ = ?
S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$
$570.72 = 820 ({100 - 20}/100)({100 - D_2}/100)$
$5707200/{820 × 80} = 100 - D_2$
$100 - D_2 = 87 ⇒ D_2$ = 13%
Q-11) The difference between a discount of 30% on Rs.2,000 and two successive discounts of 25% and 5% on the same amount is
(a)
(b)
(c)
(d)
Using Rule 5,
Case I,
Discount = ${30 × 2000}/100$ = Rs.600
Single equivalent discount for discounts of 25% and 5%.
= $(25 + 5 - {25 × 5}/100)$%
= (30 - 1.25)% = 28.75%
Discount = ${28.75 × 2000}/100$ = Rs.575
Difference = Rs.(600 - 575) = Rs.25
Q-12) A trader sells his goods at a discount of 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be
(a)
(b)
(c)
(d)
Let the marked price = Rs.100
S.P = Rs.80
Profit = 25%
CP = Rs.$(100/125 × 80)$ = Rs.64
Profit after selling on marked price
= 100 - 64 = Rs.36
Gain % = $36/64 × 100$ = 56.25%
Using Rule 6,
Here, D = 20% r = 25%
Let, M.P. be Rs.100
$\text"MP"/\text"CP" = {100 + r}/{100 - D}$
$100/\text"CP" = {100 + 25}/{100 - 20}$
C.P. = ${100 × 80}/125$
C.P. = Rs.64
Profit = 100 - 64 = 36
Gain % = $36/64 × 100%$ = 56.25%
Q-13) A shopkeeper buys an article for Rs.180. He wishes to gain 20% after allowing a discount of 10% on the marked price to the customer. The marked price will be
(a)
(b)
(c)
(d)
SP = $180 × 120/100$ = Rs.216
90% = 216
100% = $216/90 × 100$ = Rs.240
Q-14) The true discount on Rs.1, 860 due after a certain time at 5% is Rs.60. Find the time after which it is due.
(a)
(b)
(c)
(d)
Present worth
= 1860 - 60 = Rs.1800
Time = ${100 × \text"True Discount"}/\text"Present worth × Rate"$
= ${100 × 60}/{1800 × 5} = 2/3$ year
= $(2/3 × 12)$ months = 8 months
Q-15) By giving a discount of 10% on the marked price of Rs.1100 of a cycle, a dealer gains 10%. The cost price of the cycle is :
(a)
(b)
(c)
(d)
Selling Price
= Rs.(1100 - 10% of 1100)
= Rs.(1100 - 110) = Rs.990
Let the cost price = x
x + 10% of x = 990
${11x}/10$ = 990
$x = {990 × 10}/11$ = Rs.900
Using Rule 6,
Here, r = 10%, D = 10%, M.P. = Rs.1100, C.P. = ?
$\text"MP"/\text"CP" = {100 + r}/{100 - D}$
$1100/\text"CP" = {100 + 10}/{100 - 10}$
C.P. = ${1100 × 90}/110$ = Rs.900
Q-16) A profit of l0% is made after giving a discount of 5% on a T. V. If the marked price of the TV is Rs.2640.00, the cost price of the TV was :
(a)
(b)
(c)
(d)
Let the C.P. of TV be x, then
${x × 110}/100 = 2640 × 95/100$
$x = {2640 × 95}/110$ = Rs.2280
Using Rule 6,
Here, r = 10%, D = 5%,
M.P. = Rs.264000,C.P. = ?
$\text"MP"/\text"CP" = {100 + r}/{100 - D}$
$2640/\text"CP" = {100 + 10}/{100 - 5}$
C.P. = ${2640 × 95}/110$
= 24 × 95 = 2280
Q-17) 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)
(b)
(c)
(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$3/8$%
Q-18) 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)
(b)
(c)
(d)
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
$x = 100/12 = 25/3 = 8{1}/3$%
Q-19) 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)
(b)
(c)
(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
Q-20) List price of an article at a show room is Rs.2,000 and it is being sold at successive discounts of 20% and 10%. Its net selling price will be :
(a)
(b)
(c)
(d)
Equivalent discount for successive discounts of 20% and 10%
= $[20 + 10 - {20 × 10}/100]%$ = 28%
Net selling price = 72% of 2000
= Rs.${72 × 2000}/100$ = Rs.1440
Using Rule 3,
Here, M.P. = Rs.2000, $D_1 = 20%, D_2$ = 10%
S.P. = M.P.$[({100 - D_1}/100)({100 - D_2}/100)]$
= M.P.$[2000 × ({100 - 20}/100) × ({100 - 10}/100)]$
= $2000 × {80 × 90}/10000$ = Rs.1440