Practice Problems on successive discount - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) 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-2) Successive discounts of 10% and 30% are equivalent to a single discount of :
(a)
(b)
(c)
(d)
Using Rule 5,
Equivalent discount
= 30 + 10 - ${30 × 10}/100$ = 37%
Q-3) 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-4) 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-5) 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-6) 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-7) 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-8) 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-9) 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-10) 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%