Profit And Loss - Study Mode
[#191] The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount on the set of the shirt and trousers is 30%, the discount offered on the trousers is = ?
Correct Answer
(C) 25%
Explanation
Solution: Let the marked price of the shirt and trousers be Rs. x and Rs. 2x respectively. Let the discount offered on trousers be y% Then, Selling price of shirt $$eqalign{
& = 60\% { ext{ of Rs}}{ ext{. }}x cr
& = { ext{Rs}}left( {frac{{60}}{{100}} imes x}
ight) cr
& = { ext{Rs}}{ ext{.}}frac{{3x}}{5} cr
& { ext{Selling price of trousers}} cr
& = left( {100 - y}
ight)\% { ext{ of Rs}}{ ext{. }}2x cr
& = { ext{Rs}}.left[ {frac{{left( {100 - y}
ight)}}{{100}} imes 2x}
ight] cr
& = { ext{Rs}}.left[ {frac{{left( {100 - y}
ight)x}}{{50}}}
ight] cr} $$ Combined Selling price of shirt and trousers $$eqalign{
& = 70\% { ext{ of Rs}}{ ext{.}}left( {x + 2x}
ight) cr
& = { ext{Rs}}.left( {frac{{70}}{{100}} imes 3x}
ight) cr
& = { ext{Rs}}.frac{{21x}}{{10}} cr
& herefore frac{{3x}}{5} + frac{{left( {100 - y}
ight)x}}{{50}} = frac{{21x}}{{10}} cr
& Rightarrow frac{{130 - y}}{{50}} = frac{{21}}{{10}} cr
& Rightarrow 1300 - 10y = 1050 cr
& Rightarrow y = 25 cr} $$
[#192] A shopkeeper offered a discount of 15% on the labelled price. By selling an article for Rs. 340 after giving discount he earned a profit of $$13frac{1}{3}$$% . What would have been the percent profit earned if no discount was offered?
Correct Answer
(D) $$33frac{1}{3}$$
Explanation
Solution: $$eqalign{
& { ext{S}}{ ext{.P}}{ ext{.}} = { ext{Rs}}{ ext{.340}}{ ext{}} cr
& { ext{Let marked price be Rs}}{ ext{. }}x{ ext{.}} cr
& { ext{Then,}} cr
& { ext{ = 85}}\% { ext{ of }}x = { ext{340}} cr
& Rightarrow x{ ext{ = }}left( {frac{{340 imes 100}}{{85}}}
ight) = 400 cr
& { ext{Cost Price}} cr
& = { ext{Rs}}{ ext{.}}left( {100 imes frac{3}{{340}} imes 340}
ight) cr
& = { ext{Rs}}{ ext{. 300}}{ ext{.}} cr
& { ext{Now, C}}{ ext{.P}}{ ext{. = Rs}}{ ext{. 300}}{ ext{}} cr
& { ext{S}}{ ext{.P}}{ ext{.}} = { ext{Rs}}{ ext{. 400}}{ ext{}} cr
& herefore { ext{ Required profit }}\% cr
& = left( {frac{{100}}{{300}} imes 100}
ight)\% cr
& = 33frac{1}{3}\% cr} $$
[#193] A lady buys grocery worth Rs. 350 from a shop. The shopkeeper is selling the goods with zero profit. The lady gives him Rs. 2000 note. The shopkeeper gets the change from the next shop, keeps 350 for himself and returns Rs.1650 to the lady. Later, the shopkeeper of the next shop comes with Rs. 2000 note saying that it is a duplicate note and takes his money back. How much loss did the shopkeeper face?
Correct Answer
(C) Rs. 2000
Explanation
Solution: Step - 1. Start with the assumption that the shopkeeper has Rs. 10000 in his cash (this is just for making it simple). Step - 2. The lady comes in and shops for Rs. 350 and gives the shopkeeper Rs. 2000. Then, the shopkeeper now has Rs. 10000 + 2000 = Rs. 12000 in cash. Step - 3 . The shopkeeper takes the Rs. 2000 Note to another shopkeeper and gets Rs. 2000 in change - therefore he still has Rs. 12000 in cash as in step 2. Step - 4 . Now the shopkeeper gives Rs. 1650 back to the lady. So the shopkeeper is now left with 12000 - 1650 = Rs. 10350 in cash. Step - 5. Now the other shopkeeper comes in with the duplicate note and takes his money back. The duplicate note has zero value. So basically now the shopkeeper is down to 10350 - 2000 = Rs. 8350 Step - 6. He originally had Rs. 10000 in cash. Now has Rs. 8350, So Rs. 1650 loss, plus 350 lost in the grocery that the lady took. Step - 7. Total loss Rs. 1650 + 350 = Rs. 2000.
[#194] A lady buys goods worth Rs. 200 from a shop. (shopkeeper is selling the goods with zero profit). The lady gives him a Rs. 1000 note. The shopkeeper gets the change from the next shop and keeps Rs. 200 for himself and returns Rs.800 to the lady. Later the shopkeeper of the next shop comes with the Rs.1000 note saying “duplicate” and takes his money back.
How much LOSS did the shopkeeper face?
Correct Answer
(C) Rs. 1000
Explanation
Solution: Let us assume that the shopkeeper has Rs. 1000 currency Extra with his Rs. 200 worth Goods. Step - 1. Shopkeeper → Rs. 200 worth goods + Rs. 1000 Original Currency. Lady → Rs. 1000 fake currency. Neighbor → Rs. 1000 as changes. Step - 2. Shopkeeper → Rs. 1000 fake currency + Rs. 1000 Original Currency. Lady → Rs. 200 worth goods. Neighbor → Rs. 1000 as changes Step - 3. Shopkeeper → Rs. 1000 as changes + Rs. 1000 Original Currency. Lady → Rs. 200 worth goods. Neighbor → Rs. 1000 fake currency Step - 4. Shopkeeper → Rs. 200 + Rs.1000 Original Currency Lady → Rs. 200 worth goods + Rs. 800 Neighbor → Rs. 1000 fake currency Step - 5. Shopkeeper → Rs. 200 + Rs. 1000 fake currency Lady → Rs. 200 worth goods + Rs. 800 Neighbor → Rs. 1000 Original Currency Compare Step 1 and Step 5 now.
Lady changed her Rs. 1000 fake currency into goods and currency of total worth Rs. 1000
The shopkeeper changed his Original Rs. 1000 currency into a fake currency.
So the loss for the shopkeeper is Rs. 1000.
[#195] A shopkeeper sells his items using a faulty balance which measures 25% less. He then marks up his items 15% above the cost price. If he also gives a discount of 10%, then find his net profit percentage on 1 kg items
Correct Answer
(D) 38%
Explanation
Solution: $$eqalign{
& frac{{MP}}{{CP}} = frac{{115}}{{100}} cr
& frac{{MP}}{{CP}} = frac{{100 + P}}{{100 - d}},,,,left( {d\% = 10\% }
ight) cr
& Rightarrow frac{{115}}{{100}} = frac{{100 + P}}{{100 - 10}} cr
& Rightarrow frac{{23}}{{20}} = frac{{100 + P}}{{90}} cr
& Rightarrow P\% = 3.5\% cr
& { ext{Now, According to the question he weights }}25\% { ext{ less}} cr
& 25\% = frac{1}{4} cr
& frac{{SP}}{{CP}} = frac{4}{3} imes frac{{103.5}}{{100}} = frac{{69}}{{50}} cr
& { ext{Profit }}\% = frac{{19}}{{50}} imes 100 = 38\% cr} $$