Question Detail

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x

Answer: Option D

Explanation:

Let the Cost Price of one article = Rs. 1
CP of x articles = Rs. x
CP of 20 articles = 20
Selling price of x articles = 20

Profit = 25% [Given]

\begin{aligned}
\Rightarrow \left (\dfrac{SP - CP }{CP}\right ) = \dfrac{25}{100} = \dfrac{1}{4}

& \Rightarrow \dfrac{\left(20-x \right )}{x} = \dfrac{1}{4} \\
& \Rightarrow 80 - 4x = x \\
& \Rightarrow 5x = 80 \nonumber \\
& \Rightarrow x = \dfrac{80}{5} = 16 \\

\end{aligned}

1. A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 21 per kg, then his gain percent is

Answer: Option A

Explanation:

Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 21) = Rs. 168.
Profit = 168 - 150 = 18

So, Profit % = (18/150) * 100 = 12%

2. A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is.

Answer: Option B

Explanation:

\begin{aligned}
Gain\% = \\ \left( \frac{(100 + \text{common gain}\%)^2}{100} - 100 \right)\% \\
= \left( \frac{(100 + 10)^2}{100} - 100 \right)\% \\
= \left( \frac{12100 - 10000}{100}\right)\% \\
= 21\%

\end{aligned}

3. A man gains 20% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.

130%
140%
150%
160%

Answer: Option B

Explanation:

Let the C.P. = x,
Then S.P. = (120/100)x = 6x/5
New S.P. = 2(6x/5) = 12x/5

Profit = 12x/5 - x = 7x/5

Profit% = (Profit/C.P.) * 100
=> (7x/5) * (1/x) * 100 = 140 %

4. A man buys an article for Rs. 27.50 and sells it for Rs 28.60. Find his gain percent

Answer: Option D

Explanation:

So we have C.P. = 27.50
S.P. = 28.60

Gain = 28.60 - 27.50 = Rs. 1.10

\begin{aligned}
Gain\% = \left( \frac{Gain}{Cost} * 100 \right)\% \\
= \left( \frac{1.10}{27.50} * 100 \right)\% = 4\%
\end{aligned}

5. In terms of percentage profit, which among following the best transaction.

C.P. 36, Profit 17
C.P. 50, Profit 24
C.P. 40, Profit 19
C.P. 60, Profit 29

Answer: Option D

Explanation:

Hint: Calculate profit percent as

Profit% = (profit/cost) * 100