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31. A trader wishes to gain 20% after allowing 10% discount on the marked price to his customers. At what percent higher than the cost price must he mark his goods ?

A. 30%

B. $33 \frac{1}{3} %$

C. $34 \frac{2}{3} %$

D. 35%

Discuss

Solution:

Let the cost price of goods = Rs. 100
Selling price of goods
= 120% of 100
= Rs. 120
Mark price of goods

\begin{aligned} =  120 \times \frac{100}{90} \\ = \frac{400}{3} \end{aligned}

Difference of Mark price and Cost price

\begin{aligned} = \frac{400}{3} - 100 \\ Difference % \\ = \frac{\frac{100}{3}}{100} \times 100 \\ = \frac{100}{3} % \\ = 33 \frac{1}{3} % \end{aligned}

32. In order to maintain the price line a trader allows a discount of 10% on the marked price of an article. However, he still makes a profit of 17% on the cost price. Had he sold the article at the marked price, he would have earned a profit percent of = ?

A. 30%

B. 32%

C. 33%

D. 35%

Discuss

Solution:

CP	SP	MP
100_×10	117_×10
	90_×13	100_×13
1000	1170	1300

\begin{aligned} ∴ L .C .M of 117 and 90 \\ Profit = 1300 - 1000 \\ =  Rs . 300 \\ Profit = \frac{300}{1000} \times 100 \\ = 30% \end{aligned}

33. A shopkeeper sells a badminton racket whose marked price is Rs. 30, at a discount of 15% and gives a shuttle cock costing Rs. 1.50 free with each racket. Even then he makes a profit of 20%. His cost price, per racket is = ?

A. Rs. 21.00

B. Rs. 21.25

C. Rs. 20.00

D. Rs. 17.75

Discuss

Solution:

Mark price of racket = Rs. 30
After discount selling price = 85% of Rs. 30

\begin{aligned} = \frac{85}{100} \times 30 \\ = Rs . 25 .50 \\ Selling price of racket \\ = 25 .50 - 1 .50 \\ = Rs . 24 \\ Cost price of racket \\ = 24 \times \frac{100}{120} \\ = Rs . 20 \end{aligned}

34. A person paid Rs. 17000 for a motor-car after a single discount of 15%. If he is given successive discount of 5% and 10% then how much he would pay ?

A. Rs. 17000

B. Rs. 17010

C. Rs. 17100

D. Rs. 18900

Discuss

Solution:

Cost price of motor-car = Rs. 17000
Mark price of motor-car

\begin{aligned} = Rs . 17000 \times \frac{100}{85} \\ = Rs . 20000 \end{aligned}

After successive discount,Cost price

\begin{aligned} = Rs . 20000 \times \frac{95}{100} \times \frac{90}{100} \\ = Rs . 17100 \end{aligned}

35. A store has an offer 'Buy 4 Get 1 Free'. What is the net percentage of discount ?

A. 25%

B. 33.3%

C. 20%

D. Insufficient Data

Discuss

Solution:

Let, Marked price of the thing is Rs. 100

SP	Discount	MP
400	100	500

\begin{aligned} ∴ Discount % \\ = \frac{100}{500} \times 100 \\ = 20 % \end{aligned}

36. A shopkeeper offers 10% discount on the marked price of his articles and still makes a profit of 20%. What is the actual cost of the article marked Rs. 500 for him ?

A. Rs. 440

B. Rs. 425

C. Rs. 400

D. Rs. 375

Discuss

Solution:

\begin{aligned} Marked price of article \\ = Rs . 500 \\ Selling price of article \\ = 90% of 500 \\ = \frac{90}{100} \times 500 \\ = Rs . 450 \\ Cost price of article \\ = 450 \times \frac{100}{120} \\ = Rs . 375 \end{aligned}

37. A shopkeeper gives two successive discounts on an article marked Rs. 450. The first discount given is 10 percent. If the customer pays Rs. 344.25 for the article, the second discount gives is = ?

A. 14%

B. 10%

C. 12%

D. 15%

Discuss

Solution:

\begin{aligned} Marked price of an article \\ = Rs . 450 \\ After 1st discount \\ = 450 \times \frac{90}{100} \\ = Rs . 405 \\ Cost price of an article \\ = Rs . 344 .25 \\ Difference \\ = Rs . 405 - 344.25 \\ = Rs . 60 .75 \\ 2nd discount \\ = \frac{60.75}{405} \times 100 \\ = 15 % \end{aligned}

38. A man sells a bicycle at marked price which is 30% higher than the cost price. If he gives some discount and sells it at Rs. 150 less than the marked price, he would still gain 20%. What is the percentage of discount offered ?

A. 7.69%

B. 1.83%

C. 7.54%

D. 7.23%

Discuss

Solution:

\begin{matrix} 30 % = \frac{3^{↗^{gain}}}{10_{↘_{cost price}}} marked price = 13 \\ 20 % = \frac{1^{↗^{profit}}}{5_{↘_{cost price}}} selling price = 6 \end{matrix}

\begin{matrix} \begin{matrix} Cost price & Selling price & Marked price \\ 10 & 13 \\ 5 \times 2 & 6 \times 2 \end{matrix} \\ \bar{10 units \underset{discount  =  1}{\underset{⏟}{12 1 3  unit}}} \end{matrix}

\begin{aligned} ∴ Discount % \\ = \frac{1}{13} \times 100 \\ = 7.69 % \end{aligned}

39. Rakesh yadav buys an article with a discount of 25% on its marked price. He makes a profit of 10% by selling it at Rs. 660. The marked price of the article was ?

A. Rs. 600

B. Rs. 700

C. Rs. 800

D. Rs. 685

Discuss

Solution:

Selling price of an article = Rs. 660

\begin{aligned} Cost price of an article \\ = 660 \times \frac{100}{110} \\ = Rs . 600 \\ Marked price of an article \\ = 600 \times \frac{100}{75} \\ = Rs . 800 \end{aligned}

40. A dealer buys an article marked at Rs. 25000 with 20% and 5% off. He spends Rs. 1000 for its repair and sells it for Rs. 25000 what is his gain or loss percent ?

A. Loss of 25%

B. Gain of 25%

C. Gain of 10%

D. Loss of 10%

Discuss

Solution:

Marked price of an article = Rs. 25000
After discount, cost price

= Rs . 25000 \times \frac{80}{100} \times \frac{95}{100}

= Rs. 19000
After repair, cost price
= Rs. 19000 + 1000
= Rs. 20000
Selling price of an article = Rs. 25000

\begin{aligned} Gain % \Rightarrow \frac{25000 - 20000}{20000} \times 100 \\ Gain % \Rightarrow \frac{1}{4} \times 100 \\ Gain % \Rightarrow 25 % \end{aligned}

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