Question

A shopkeeper sells two qualities of wheat at the rates of $11 per kg. and $24 per kg, gaining 10% and 20% profit respectively. If he mixes the two variants in the ratio 2:3 and sells the mixture at $12.8 per kg., what is his gain% or loss%?


A) 20%profit B) 20%loss C) 25%loss D)25%profit


Please also explain how you got the answer.

Thanks in advance^_^

Answer 1

Answer:b. 20% loss

Step-by-step explanation:

Step 1

Let the cost price of two qualities of wheat be $x and $y per kg respectively.

The profit on selling each of them is 10% and 20% respectively.

Step 2

As we know,

Selling Price = Cost Price + Profit

So, selling price of first quality of wheat = x + 10% of x = $11

⇒ x +  

10

100

 × x = $11

⇒ x +  $xVar

10

 = $11

⇒  11x

10

 = $11

⇒ x = $11 ×  10

11

⇒ x = $10

Step 3

Selling price of second quality of wheat = y + 20% of y = $24

⇒ y +  $yVar

5

 = $24

⇒  6y

5

 = $24

⇒ y = $24 ×  5

6

⇒ y = $20

Step 4

These two qualities of wheat are mixed in the ratio of 2:3 by weight, which means in 1 kg of the new mixture of wheat, there is  2

5

 × 1 = 0.4 kg of wheat of the first type and  3

5

 × 1 = 0.6 kg of wheat of the second type respectively.

Step 5

Since 1 kg of first quality of wheat costs $10.

0.4 kg will cost = 10 × 0.4 = $4

Step 6

Similarly 1 kg of the second quality of wheat costs $20.

0.6 kg will cost = 20 × 0.6 = $12

Step 7

We can see that the cost price of 1 kg of the mixture = $4 + $12 = $16

Step 8

The selling price of the mixture is $12.8 per kg.

Thus, the shopkeeper incures a loss.

Loss = cost price - selling price = $16 - $12.8 = $3.2

Step 9

The loss percent =  loss

Cost Price

 × 100% =  $3.2

$16

 × 100% = 20%

Step 10

Thus, the shopkeeper had a loss of 20%

Answer 2

${\huge {\mathfrak {\orange {Answer :-}}}}$

The shopkeeper sells two kinds qualities of wheat at 11 per kg and 24 per kg.

➡️ On the $11, he gains 10% profit.

Let the cost price be x.

So, x + 10/100 * x = 11

Or, x + x/10 = 11

Or, 11x/10 = 11

Or, x = 10.

So, cost price of the first quality of wheat is $10. ⬅️

➡️ On the $24, he gains 20% profit.

Let the cost price be y.

So, y + 20/100 * y =24

Or, y + y/5 = 24

Or, 6y/5 = 24

Or, y = 24 * 5/6 = 20.

So, the Cost price of second quality of the wheat is $20. ⬅️

$<b>$ He mixes them is the ratio 2 : 3.

Now, sum of ratios is = 5.

Thus, 2/5 part is the wheat of first quality and 3/5 part is the wheat of second quality.

Thus, Cost price of the mixture

= $ (2/5 * 10 + 3/5 * 20)

= $ (4 + 12)

= $ 16.

➡️ Again, the shopkeeper sells it at $12.8 per kg.

So, it is obvious that Cost price > Selling price, so there is a loss.

Loss = $ (16 - 12.8)

= $ 3.2

Now, Loss percentage

= 3.2/16 * 100 %

= 1/5 * 100 %

= 20 %

➡️ Hence, there is a loss of 20%

➡️ Option (B) 20% loss.

$</b>$ $<i>That's it.. </i>$

${\red{-:Arnab \: Here:-}}$
$<marquee>$
${\huge {\blue {Thanks}}}$