Profit And Loss - Study Mode

[#271] Manish purchased 25 kg of rice @ Rs. 32 per kg and 15 kg of rice @ Rs. 36 per kg. He mixed the two varieties of rice and sold it @ Rs. 40.20 per kg. What is the percent profit earned ?
Correct Answer

(A) 20%

Explanation

Solution: $$eqalign{
& { ext{C}}{ ext{.P}}{ ext{. of 40 kg rice}} cr
& = { ext{Rs}}.left( {25 imes 32 + 15 imes 36}
ight) cr
& = { ext{Rs}}.left( {800 + 540}
ight) cr
& = { ext{Rs}}.1340. cr
& { ext{S}}{ ext{.P}}{ ext{. of 40 kg rice}} cr
& = { ext{Rs}}.left( {40 imes 40.20}
ight) cr
& = { ext{Rs}}{ ext{. }}1608. cr
& { ext{Profit}} = { ext{Rs}}.left( {1608 - 1340}
ight) cr
& ,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{. }}268. cr
& herefore { ext{Profit }}\% = left( {frac{{268}}{{1340}} imes 100}
ight)\% cr
& ,,,,,,,,,,,,,,,,,,,,,,,,, = 20\% cr} $$

[#272] Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of Rs. 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit ?
Correct Answer

(D) Rs. 16.30

Explanation

Solution: C.P. of 50 kg wheat = Rs. (30 × 11.50 + 20 × 14.25) = Rs. (345 + 285) = Rs. 630 $$eqalign{
& { ext{S}}{ ext{.P}}{ ext{. of 50 kg wheat}} cr
& = 130\% { ext{ of Rs}}{ ext{.630}} cr
& = { ext{Rs}}.left( {frac{{130}}{{100}} imes 630}
ight) cr
& = { ext{Rs}}.819 cr
& herefore { ext{S}}{ ext{.P}}{ ext{. per kg}} cr
& = { ext{Rs}}{ ext{.}}left( {frac{{819}}{{50}}}
ight) cr
& = { ext{Rs}}.16.38 approx { ext{Rs}}.16.30 cr} $$

[#273] A dealer buys dry fruit at the rate of Rs. 100, Rs. 80 and Rs. 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity ?
Correct Answer

(C) 40%

Explanation

Solution: Suppose he bought 12 kg, 15 kg and 20 kg of the three varieties respectively. Then, Total C.P. = Rs. (12 × 100 + 15 × 80 + 20 × 60) = Rs. (1200 + 1200 + 1200) = Rs. 3600 Let the loss on the third quantity be x% Than, =120% of 2400 +(100 - x)% of 1200 = 3600 $$eqalign{
& Rightarrow left( {frac{6}{5} imes 24}
ight) + left( {frac{{100 - x}}{{100}} imes 12}
ight) = 36 cr
& Rightarrow frac{{100 - x}}{{100}} imes 12 = 36 - frac{{144}}{5} = frac{{36}}{5} cr
& Rightarrow frac{{100 - x}}{{100}} = frac{{36}}{5} imes frac{1}{{12}} = frac{3}{5} cr
& Rightarrow 500 - 5x = 300 cr
& Rightarrow 5x = 200 cr
& Rightarrow x = 40\% cr} $$

[#274] A man purchased an article for Rs. 1500 and sold it at 25% above the cost price. If he has to pay Rs. 75 as tax on it his net profit percentage will be = ?
Correct Answer

(D) 20%

Explanation

Solution: $$eqalign{
& { ext{Cost price}} = { ext{Rs}}{ ext{. 1500}} cr
& { ext{Profit after selling}} cr
& = 25\% { ext{ of }}1500 cr
& = { ext{Rs}}{ ext{.375}} cr
& { ext{Net profit }} cr
& = { ext{Rs}}{ ext{.375}} - { ext{Rs}}{ ext{.75}} cr
& = { ext{Rs}}{ ext{.300}} cr
& { ext{Net profit }}\% cr
& = frac{{300}}{{1500}} imes 100 cr
& = 20\% cr} $$

[#275] By selling some goods at Rs. 31, a salesman loses 7% on his output. Find the percentage profit of loss, when he sells the same at Rs. 35 = ?
Correct Answer

(B) Profit 5%

Explanation

Solution: Selling price of goods = Rs. 31 Cost price of goods $$eqalign{
& = { ext{31}} imes frac{{100}}{{93}} cr
& = { ext{Rs}}{ ext{. }}frac{{100}}{3} cr
& { ext{Profit }}\% cr
& = frac{{35 - frac{{100}}{3}}}{{frac{{100}}{3}}} imes 100 cr
& = frac{{frac{5}{3}}}{{frac{{100}}{3}}} imes 100 cr
& = 5\% cr} $$