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

$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{125}}{{100}} \times 40} \right) \cr & = {\text{Rs}}{\text{. }}50 \cr & {\text{S}}{\text{.P}}{\text{.of each pen}} \cr & = {\text{Rs}}.\left( {\frac{{50}}{{100}}} \right) \cr & = {\text{50 paise}}{\text{}} \cr} $$