## Profit and Loss Questions and Answers Part-10

1. The price of an article reduces to 576 after two successive discounts. The markup is 80% above the cost price of Rs. 500. What is the new profit percentage if instead of two successive discounts the markup price was further increased successively two times by the same percentage?
a) 259.2%
b) 157%
c) 159.2%
d) 300%

Explanation
\eqalign{ & {\text{CP}} = 500 \cr & {\text{SP}} = 576 \cr & {\text{MP}} = 900\left[ {80\% \,{\text{above}}\,{\text{the}}\,{\text{CP}}} \right] \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & \left[ {{\text{R = Rate}}\,{\text{of}}\,{\text{Discount}}} \right] \cr & 576 = 900 \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & R = 20\% \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 + {\frac{R}{{100}}} } \right]^2} \cr & {\text{SP}} = 900 \times {\left[ {1 + {\frac{{20}}{{100}}} } \right]^2} \cr & {\text{SP}} = 1296 \cr & {\text{New}}\,{\text{Profit}}\,{\text{Percentage}}, \cr & = {\frac{{ {SP - CP} }}{{CP}}} \times 100 \cr & = {\frac{{ {1296 - 500} }}{{500}}} \times 100 \cr & = 159.2\% \cr}

2. A dishonest trader marks up his goods by 80% and gives discount of 25%. Besides he gets 20% more amount per kg from wholesaler and sells 10% less per kg to customer. What is the overall profit percentage?
a) 50%
b) 60%
c) 70%
d) 80%

Explanation: CP = $$\frac{{100}}{{120}} = \frac{{10}}{{12}}$$   [He purchases 120 g and pays Rs. 100, by assumption actual CP of 1 g = Re. 1]
SP = $$\frac{{135}}{{90}} = \frac{3}{2} = \frac{{18}}{{15}}$$    [Actual MP = 180 as he mark up 80% above, SP = 135, with 25% discount and he sells 90 g instead of 100g]
Percentage Profit = $${\frac{{\frac{{18}}{{12}} - \frac{{10}}{{12}}}}{{\frac{{10}}{{12}}}}} \times 100 = 80\%$$

3. The profit percentage on three articles A, B and C is 10%, 20%, and 25% and the ratio of the cost price is 1 : 2 : 4. Also the ratio of number of articles sold of A, B and C is 2 : 5 : 2, then overall profit percentage is:The profit percentage on three articles A, B and C is 10%, 20%, and 25% and the ratio of the cost price is 1 : 2 : 4. Also the ratio of number of articles sold of A, B and C is 2 : 5 : 2, then overall profit percentage is:
a) 18.5%
b) 21%
c) 23%
d) 27%

Explanation: Ratio of CP = 1 : 2 : 4
Let cost of,
A = x
B = 2x
C = 4x
Ratio of Number of sell = 2 : 5 : 2
Let number of items sold be,
A = 2y
B = 5y
C = 2y
Total cost (A + B + C),
= (2xy + 10xy + 8xy)
= 20xy
Profit of A = 0.2xy
Profit of B = 2xy
Profit of C = 2xy
Total profit = 4.2xy
% Profit = $$\frac{{4.2{\text{xy}} \times 100}}{{20{\text{xy}}}} = 21\%$$

4. The accountants of a company show sales of Rs. 12,600. The primary cost is 35% of sales and trading cost accounts for 25% of the gross profit. Gross profit is arrived at by excluding the primary cost plus the cost of advertising expenses of Rs. 1400, director's salary of Rs. 650 per annum plus 2% annual sales as miscellaneous costs. Find the percentage profit (approx) on a capital investment of Rs. 14,000?
a) 35%
b) 31%
c) 28%
d) 26%

Explanation: Primary Cost:
35% of 12600 = 4410
Miscellaneous costs:
2% of 12600 = 252
Gross Profit = 12600 - 4410 - 1400 - 650 - 252 = 5888
Trading Cost = 0.25 × 5888 = 1472
Net Profit = 4416
% Profit =$$\frac{{4416}}{{14000}} \times100$$
= 31.54%
≈ 31%

5. A dishonest shopkeeper, at the time of selling and purchasing, weighs 10% less and 20% more per kilogram respectively. Find the percentage profit earned by treachery. (Assuming he sells at Cost Price)
a) 30%
b) 20%
c) 25%
d) 33.33%

Explanation: While purchasing he would take 1200 grams for the price of 1000 grams. While selling he would sell 900 grams for the price of 1000 grams.
Since, CP = SP
Profit =
$$\frac{{{\text{Goods Left}}}}{{{\text{Goods Sold}}}} = \frac{{300 \times 100}}{{900}} =$$       $$33.33\%$$

6. David sells his Laptop to Goliath at a loss of 20% who subsequently sells it to Hercules at a Profit of 25%. Hercules, after finding some defect in the laptop, returns it to Goliath but could recover only Rs. 4.50 for every Rs. 5 he had paid. Find the amount at Hercules' loss if David had paid Rs. 1.75 lakh for the laptop.
a) 3500
b) 2500
c) 17500
d) 20000

Explanation: David (100) == 20% ↓(loss) ⇒ Goliath (80) == 25% ↑(gain) ⇒ Hercules(100) == 10% ↓ (loss) ⇒ Goliath (90)
Hercules loss corresponds to 10 when David buys the laptop for Rs. 100.
Thus, Hercules loss would be Rs. 17,500 when David buys the laptop for 1,75,000.

7. The cost of servicing of a Maruti car at Maruti care Pvt. Ltd. is Rs. 400. Manager of service centre told me that for the second service within a year a customer can avail a 10% discount and further for third and fourth servicing he can avail 10% discount of the previous amount paid, within a year. Further if a customer gets more than 4 services within a year, he has to pay just 60% of the servicing charges on these services. A customer availed 5 services from the same servicing station, what is the total percentage discount fetched by the customer?
a) 19.42%
b) 18.5%
c) 17.6%
d) 26%

Explanation: Amount paid in 1st service = 100 (Assume)
Amount paid in 2nd service = 90
Amount paid in 3rd service = 81
Amount paid in 4th service = 72.9
Amount paid in 5th service = 60
Total amount paid,
= (100 +90 +81 +72.9 +60) = 403.9
Total Discount = 500 - 403.9 = 96.1
% Discount = $$\frac{{96.1 \times 100}}{{500}}$$   = 19.42%

8. A vendor sells his articles at a certain profit percentage. If he sells his article at $$\frac{1}{3}$$ of his actual selling price, then he incurs a loss of 40%. What is his actual profit percentage?
a) 72%
b) 120%
c) 80%
d) 60%

Explanation: 100 (CP) == 80%↑ ⇒ 180(SP)
$$\frac{1}{3}$$ of SP = $$\frac{180}{3}$$ = 60
Loss = 40% = 100 - 60 = 40
Hence, option (c) is correct as it gives 40% loss on CP on reducing the price to $$\frac{1}{3}$$ of CP.

9. Arun bought toffees at 6 for a rupee. How many for a rupee he should sell to gain 20%?
a) 2
b) 3
c) 4
d) 5

Explanation: CP for one toffee = $$\frac{{100}}{6}$$
SP will be 20% above the CP.
SP for one toffee = $$\frac{{100}}{6} \times 1.2 = \frac{{100}}{5} = 20$$
Thus, He should sell 5 toffee for Rs. 1 (100 paise)

10. The cost price of 19 articles is same as the selling price of 29 articles. What is loss percentage?
a) 52.3%
b) 35%
c) 34.48%
d) 30%

\eqalign{ & = \frac{{ {\left( {29x - 19x} \right) \times 100} }}{{29x}} \cr & = 34.48\% \cr}