## Profit and Loss Questions and Answers Part-8

1. A trader sells an article and loses $$12\frac{1}{2}$$%. The ratio of cost price to the selling price is -
a) 7 : 8
b) 9 : 8
c) 8 : 7
d) 8 : 9

Explanation:
\eqalign{ & {\text{Let C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}x \cr & {\text{Loss}} = 12\frac{1}{2}\% \cr & {\text{S}}{\text{.P}}{\text{.}} = 87\frac{1}{2}\% {\text{ of Rs}}{\text{. }}x \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left( {\frac{{175}}{2} \times \frac{1}{{100}} \times x} \right) \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{7x}}{8} \cr & {\text{Required ratio}} \cr & = x:\frac{{7x}}{8} = 8:7 \cr}

2. If the cost price of 18 articles is equal to the selling price of 16 articles, the gain or loss is = ?
a) 25% gain
b) 25% loss
c) $$12\frac{1}{2}$$% loss
d) $$12\frac{1}{2}$$% gain

Explanation: 18 Cost Price = 16 Selling Price
\eqalign{ & \frac{{{\text{CP}}}}{{{\text{SP}}}} = \left. {\frac{{16}}{{18}} = \frac{8}{9}} \right\}{\text{1 unit profit}} \cr & {\text{Profit}}\% = \frac{1}{8} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\frac{1}{2}\% {\text{ gain}} \cr}

3. The price of a refrigerator and a television set are in the ratio 5 : 3. If the refrigerator costs Rs. 5500 more than the television set, then the price of the refrigerator is = ?
a) Rs. 27500
b) Rs. 8250
c) Rs. 13750
d) Rs. 16500

Explanation:
\eqalign{ & \frac{{{\text{CP of Refrigerator}}}}{{{\text{CP of Television }}}}\left. { = \frac{5}{3}} \right\}{\text{2 unit }} \cr & {\text{2 unit}} = 5500 \cr & {\text{1 unit}} = \frac{{5500}}{2} = 2750 \cr & 5{\text{ units}} = 2750 \times 5 = 13750 \cr & {\text{Cost price of Refrigerator}} \cr & = {\text{Rs}}{\text{.13750}} \cr}

4. If books bought at prices from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs. 350. What is the greatest possible profit that might be made in selling 15 books ?
a) Cannot be determind
b) Rs. 750
c) Rs. 4250
d) Rs. 3000

Explanation: Cost price of a book ranges between
= Rs. 150 to 300
Selling price of a book ranges between
= Rs. 250 to 350
For maximum profit cost price should minimum and Selling price should be maximum
Cost price = 150
Selling price = 350
Profit = Selling price - Cost price
= 350 - 150
= Rs. 200/book
Total profit on 15 books
= 200 × 15
= Rs. 3000

5. A person buys an article for Rs. p and sells it for Rs. q thereby gaining r% . The selling price in terms of cost price may be written as -
a) $$\frac{{{\text{pr}}}}{{100}}$$
b) $$\frac{{{\text{r}}\left( {100 + {\text{p}}} \right)}}{{100}}$$
c) $$\frac{{{\text{p}}\left( {100 + {\text{r}}} \right)}}{{100}}$$
d) $$\frac{{{\text{p}}\left( {100 - {\text{r}}} \right)}}{{100}}$$

Explanation:
\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. p}} \cr & {\text{Gain}} = {\text{r}}\% \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{q}} \cr & = \left( {100 + {\text{r}}} \right)\% {\text{ of Rs}}{\text{. p}} \cr & = \frac{{{\text{p}}\left( {100 + {\text{r}}} \right)}}{{100}} \cr}

6. The owner of a furniture shop charges his customer 28% more than the cost price. If a customer paid Rs. 23680 for a dining table set, then what was the original price of the dining set ?
a) Rs. 15700
b) Rs. 16250
c) Rs. 17500
d) Rs. 18500

Explanation:
\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}23680 \cr & {\text{Profit}} = 28\% \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{128}} \times 23680} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}18500 \cr}

7. An article marked at Rs. 540 is sold at Rs. 496.80 in an off - season offer. Then the rate of discount offered (in percent) is = ?
a) 7%
b) 7.5%
c) 8%
d) 10%

Explanation:
\eqalign{ & {\text{Discount}} \cr & = 540 - 496.80 \cr & = 43.2 \cr & {\text{Discount }}\% \cr & = \frac{{43.2}}{{540}} \times 100 \cr & = 8\% \cr}

8. Bhuvnesh sell two tape recorders at the same price. On one, he gains 10% and on the other he loses 10%. The total gain or loss in the transaction is=?
a) 1% gain
b) 1% loss
c) No loss or gain
d) 2% loss

Explanation: In this type of question always loss
$$\frac{{P\% \times L\% }}{{100}} = \frac{{10 \times 10}}{{100}} = 1\% \,{\text{loss}}$$

9. A cloth merchant has announced 25% rebate in prices. If one needs to have a rebate of Rs. 40 then how many metres of cloth costing Rs. 32 per metre he should purchase =
a) 6m
b) 5m
c) 10m
d) 7m

\eqalign{ & x \times 32 \times \frac{{25}}{{100}} = 40 \cr & x \times 8 = 40 \cr & x = 5\,m \cr}
10. A shopkeeper expects a gain of $$22\frac{1}{2}$$% on his cost price. If in a week, his sale was of Rs. 392, what was his profit ?
\eqalign{ & {\text{C}}{\text{.P}}{\text{. = Rs}}.\left( {\frac{{100}}{{122.50}} \times 392} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\left( {\frac{{1000}}{{1225}} \times 392} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}320. \cr & {\text{Profit}} = {\text{Rs}}.\left( {392 - 320} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}72 \cr}