1. The marked price of an item is twice the cost price, discount 20% of market price and profit is 10% of selling price. Find profit percentage to cost
a) $$\frac{{100}}{9}$$%
b) $$\frac{{100}}{11}$$%
c) 11%
d) 85%
Explanation:
MP = Rs. 200
Discount = 20%
Profit = Rs. 16
SP = 200 - 20% of 200 = 200 - 40 = Rs. 160
CP = SP - profit = 160 - 16 = Rs.144
% profit = $$\frac{{16 \times 100}}{{144}} = 11.11\% = \frac{{100}}{9}\% $$
2. The marked price of an item is twice the cost price. For a gain of 15%, the discount should be:
a) 7.5%
b) 20.5%
c) 32.5%
d) 42.5%
Explanation: Let CP = Rs. 100
MP = Rs. 200
Gain = 15%
SP = 100 + 15% of 100 = Rs. 115
Discount = 200 - 115 = 85
% Discount = $$\frac{{85 \times 100}}{{200}}$$ = 42.5%
3. A man sold his watch at a loss of 5%. Had he sold it for Rs. 56.25 more, he would have gained 10%. What is the cost price of the watch (in Rs.)?
a) 365
b) 370
c) 375
d) 390
Explanation: He sold his watch at loss of 5%. If he sells his watch for Rs. 56.25 more, he would gain 10%.
15% = Rs. 56.25.
1% = $$\frac{{56.25}}{{15}}$$
100% = $$\frac{{56.25 \times 100}}{{15}}$$ = Rs. 375
The cost price of the watch is Rs. 375
4. A total profit of Rs. 3,600 is to be distributed amongst A, B and C such that A : B = 5 : 4 and B : C = 8 : 9. The share of C in the profit is :
a) 1200
b) 1500
c) 1650
d) 1700
Explanation: A Total Profit = Rs. 3600
Profit ratio,
A : B = 5 : 4
B : C = 8 : 9
As B is common in both ratio, we make B equal in both ratio by multiplying One B in another.
A : B = 5 : 4 × 8
B : C = 8 × 4 : 9
So, ratio of
A : B : C = 40 : 32 : 36 = 10 : 8 : 9
C shares in profit = $$\frac{{3600 \times 9}}{{27}}$$ = Rs. 1200
5. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.
a) 500, 300
b) 200, 400
c) 400, 200
d) 300, 500
Explanation: Let X be the cost of horse and Y be the cost of the cart.
10% of loss in selling horse = 20% of gain in selling the cart.
$$\frac{{10}}{{100}} \times {\text{X}}$$ = (20 × 100) × Y
X = 2y --------------(1)
5% of loss in selling horse is 10 more than the 5% gain in selling the cart.
Therefore, $$\frac{5}{{100}} \times {\text{X}} - 10 = \frac{5}{{100}} \times {\text{Y}}$$
5X – 1000 = 5Y
Using equation (1),
10Y – 1000 = 5Y
5Y = 1000
Y =200
X = 400
CP of Horse = Rs. 400
CP of the Cart = Rs. 200
6. Abhishek purchased 140 shirts and 250 trousers @ Rs. 450 and @ Rs. 550 respectively. What should be the overall average selling price of shirts and trousers so that 40% profit is earned ? (rounded off to next integer)
a) Rs. 700
b) Rs. 710
c) Rs. 720
d) Rs. 725
Explanation: Total Cost Price
= Rs. (140 × 450 + 250 × 550)
$$\eqalign{ & = {\text{Rs}}.\left( {63000 + 137500} \right) \cr & = {\text{Rs}}{\text{. }}200500. \cr & {\text{Total Selling Price}} \cr & = {\text{Rs}}.\left( {\frac{{140}}{{100}} \times 200500} \right) \cr & = {\text{Rs}}{\text{. }}280700. \cr & {\text{Average Selling Price}} \cr & = {\text{Rs}}.\left( {\frac{{280700}}{{140 + 250}}} \right) \cr & = {\text{Rs}}.\left( {\frac{{280700}}{{390}}} \right) \cr & = {\text{Rs}}{\text{. }}719.74 \approx 720 \cr} $$
7. A man sells two chairs at Rs. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Rs. is = ?
a) 20
b) 16
c) 25
d) 30
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of first chair}} \cr & = \frac{{100}}{{125}} \times 120 = {\text{Rs}}{\text{.}}\,96 \cr & {\text{C}}{\text{.P}}{\text{.}}\,\,{\text{of}}\,{\text{second}}\,{\text{chair}} \cr & = \frac{{100}}{{75}} \times 120 = {\text{Rs}}{\text{.}}\,160 \cr & {\text{Loss}} = 160 + 96 - 240 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,16 \cr} $$ .
8. A man wanted to sell an article with 20% profit: but he actually sold at 20% loss for Rs. 480, at what price he wanted to sell it to earn the profit = ?
a) Rs. 720
b) Rs. 840
c) Rs. 600
d) Rs. 750
Explanation:
$$\eqalign{ & {\text{Loss }}20\% \cr & {\text{Selling price}} \cr & = 100\% - 20 = 80\% \cr & 80\% = 480 \cr & 1 = \frac{{480}}{{80}} \cr & \left( {{\text{Profit }}20\% } \right) \cr & = \frac{{480}}{{80}} \times 120 \cr & = {\text{Rs}}{\text{. }}720 \cr} $$
9. A shopkeeper sells an article at a loss of $$12\frac{1}{2}$$% . Had he sold it for Rs. 51.80 more, he would have earned a profit of 6% . The cost price of the article is = ?
a) Rs. 280
b) Rs. 300
c) Rs. 380
d) Rs. 400
Explanation: Let C.P. be Rs. x Then
(106% of x) - $$\left( {87\frac{1}{2}\% \,\,{\text{of}}\,x} \right) = 51.80$$
$$\eqalign{ & 18\frac{1}{2}\% \,\,{\text{of}}x = 51.80 \cr & x = \left( {\frac{{51.80 \times 100 \times 2}}{{37}}} \right) \cr & x = 280 \cr} $$
10. A person purchased 10 dozen pens at the rate of Rs. 4 per dozen. On checking, he found that 20 pens were not working. In order to earn 25% profit, he should sell the remaining pens each at -
a) 40 paise
b) 44 paise
c) 50 paise
d) 55 paise
Explanation: Total C.P. of (10 × 12) i.e.,
120 pens = Rs. (4 × 10) = Rs. 40
No. of working pens
= (120 - 20) = 100
Total selling price of 100 pens
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{125}}{{100}} \times 40} \right) \cr & = {\text{Rs}}{\text{. }}50 \cr & {\text{S}}{\text{.P}}{\text{.of each pen}} \cr & = {\text{Rs}}.\left( {\frac{{50}}{{100}}} \right) \cr & = {\text{50 paise}}{\text{}} \cr} $$