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41. A bicycle, marked at Rs. 2000 is sold with two successive discount of 20% and 10%. An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is = ?

A. Rs. 1368

B. Rs. 1468

C. Rs. 1568

D. Rs. 1668

Discuss

Solution:

Marked price of bicycle = Rs. 2000
After two successive discount of 20% and 10%

\begin{aligned} = 2000 \times \frac{80}{100} \times \frac{90}{100} \\ = Rs . 1440 \end{aligned}

Additional discount 5% for cash payment

\begin{aligned} = 1440 \times \frac{95}{100} \\ = Rs . 1368 \end{aligned}

42. An article is sold at a discount of 20% and an additional discount 30% is allowed on cash payment. If Vidya purchased the article by paying Rs. 2240 in cash, the marked price of the article was = ?

A. Rs. 4000

B. Rs. 4368

C. Rs. 4400

D. Rs. 4480

Discuss

Solution:

Marked price of the article = Rs. x
According to the question,

\Rightarrow

80% of 70% of x = 2240

\begin{aligned} \Rightarrow \frac{80}{100} \times \frac{70}{100} \times x = 2240 \\ \Rightarrow x = Rs . 4000 \end{aligned}

43. A retailer purchases a grinder at a discount of 15% of the whole seller and sales it for Rs. 1955 at a profit of 15%. The amount of discount received by the retailer from the whole seller was = ?

A. Rs. 720

B. Rs. 290

C. Rs. 300

D. Rs. 330

Discuss

Solution:

Selling price of grinder = Rs. 1955

\begin{aligned} Cost price of grinder \\ =  1955 \times \frac{100}{115} \\ = Rs . 1700 \\ Marked price of grinder \\ = 1700 \times \frac{100}{85} \\ = Rs . 2000 \\ Discount by the retailer \\ = 2000 \times \frac{15}{100} \\ = Rs . 300 \end{aligned}

44. The marked price of a T.V. is Rs. 16000. After two successive discounts it is sold for Rs. 11400. If the first discount is 5%, then the rate of second discount is = ?

A. 15%

B. 20%

C. 30%

D. 25%

Discuss

Solution:

Marked price of T.V. = Rs. 16000

\begin{aligned} After 1st discount \\ =  95 % of 16000 \\ = \frac{95}{100} \times 16000 \\ =  Rs . 15200 \end{aligned}

Selling price of T.V. = Rs. 11400

\begin{aligned} So, the 2nd discount be % \\ = \frac{15200 - 11400}{15200} \times 100 \\ = \frac{3800}{15200} \times 100 \\ = 25 % \end{aligned}

45. The difference between a discount of 30% on Rs. 2000 and two successive discounts of 25% and 5% on the same amount is ?

A. Rs. 30

B. Rs. 35

C. Rs. 25

D. Rs. 40

Discuss

Solution:

1st discount = 30%
Two successive discount to a single discount

\begin{aligned} = 25 + 5 - \frac{25 \times 5}{100} \\ = 30 - 1.25 \\ Difference % \\ = 30 - 30 + 1.25 \\ = 1.25 % \\ Difference amount \\ = 1.25 % of 2000 \\ = \frac{1.25}{100} \times 2000 \\ = Rs . 25 \end{aligned}

46. If on a market price the difference of selling price with a discount of 30% and two successive discounts of 20% and 10% is 72, then the marked price ( in rupees ) is ?

A. Rs. 3600

B. Rs. 3000

C. Rs. 2500

D. Rs. 2400

Discuss

Solution:

Let the marked price = Rs. x
Single Discount = 30%
Two successive discount is equivalent

\begin{aligned} = (20 + 10 - \frac{20 \times 10}{100}) % \\ = (30 - 2) % \\ = 28 % \end{aligned}

Difference = 2%
According to the question,

\begin{aligned} \Rightarrow 2 % of x =  72 \\ \Rightarrow \frac{2}{100} \times x = 72 \\ \Rightarrow x = \frac{72 \times 100}{2} \\ \Rightarrow x = Rs . 3600 \end{aligned}

47. Ramesh marks his goods 30% above cost price. If he sells the item for Rs. 910 afters allowing of 15% discount. Find his cost price ?

A. Rs. 823.5

B. Rs. 758

C. Rs. 814.2

D. Rs. 856.5

Discuss

Solution:

\begin{matrix} \begin{matrix} Cost Price & Selling Price & Mark Price \\ 10_{\times 20} & 13_{\times 20} \\ 17_{\times 13} & 20_{\times 13} \end{matrix} \\ \bar{\underline{200 unit 221 unit 260 unit}} \end{matrix}

\begin{aligned} 221 unit \to 910 \\ 260 unit \to \frac{910}{221} \times 200 \\ = Rs 823 .50 \end{aligned}

48. The single discount equivalent to two successive discount of 20% and 5% is = ?

A. 24%

B. 25%

C. 22%

D. 23%

Discuss

Solution:

Two successive discount is equivalent

\begin{aligned} = 20 + 5 - \frac{20 \times 5}{100} \\ = 25 - 1 \\ = 24 % \end{aligned}

49. A shopkeeper marks the price of an item keeping 20% profit. If he offers a discount of $12 \frac{1}{2} %$ on the marked price, his gain percent will be = ?

A. 4.5%

B. 5%

C. 7.5%

D. 8%

Discuss

Solution:

Let cost price of item = Rs. 100
Marked price of item = 120% of 100

\begin{aligned} = \frac{120}{100} \times 100 \\ =  Rs . 120 \end{aligned}

After discount, selling price = 87.5% of 120

\begin{aligned} \frac{87.5}{100} \times 120  =  Rs . 105 \\ Profit % = \frac{105 - 100}{100} \\ = 5 % \end{aligned}

50. A seller marks his goods 30% above their cost price but allows 15% discount for cash payment. His percentage of profit when sold in cash is = ?

A. 10.5%

B. 15%

C. 9%

D. 8.5%

Discuss

Solution:

Let cost price of item = Rs. 100
Marked price of item = 130% of 100

\begin{aligned} =  130 % of 100 \\ = \frac{130}{100} \times 100 \\ =  Rs . 130 \end{aligned}

After discount, selling price

\begin{aligned} =  85 % of 130 \\ = \frac{85}{100} \times 130 \\ =  Rs . 110 .5 \\ Profit % \\ = \frac{110.50 - 100}{100} \times 100 \\ = 10.5 % \end{aligned}

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