Question

Rehana went to the market and saw that the price of dal of 1 kg. is Rs 20 and the price rice of 1 kg. is Rs 40 less than that of fish of 1 kg. The quantity of fish and that of dal in Rs 240 is equal to the quantity of rice in Rs 280. Let us calculate the cost price of 1 kg. fish.​

Answer 1

Answer:

Given :-

• Rehana went to the market and saw that the price of dal of 1 kg. is 20 and the price rice of 1 kg. is Rs 40 less than that of fish of 1 kg . The quantity of fish and that of dal in Rs 240 is equal to the quantity of rice in Rs 280.

Find Out :-

• Cost price of 1 kg.

Solution :-

Suppose Rehena purchases every Kg of fish of Rs. x.

Price of Each Kg of Dal = Rs .( x - 20 ) and price of Each Kg of rice = Rs .( x - 40 )

Now,

Rs. 240 fish can be obtained = $\dfrac{240}{x}$ kg.

And, price of Rs 240 rice be obtained = $\dfrac{280}{x - 40}$ kg.

According to the question :-

⇒ $\dfrac{240}{x} + \dfrac{240}{x - 20} = \dfrac{280}{x - 40}$

⇒ $\dfrac{24}{x} + \dfrac{24}{x - 20} = \dfrac{28}{x - 40}$

⇒ $\dfrac{24}{x} = \dfrac{28}{x - 40} - \dfrac{24}{x - 20}$

⇒ $\dfrac{6}{x} = \dfrac{7}{x - 40} - \dfrac{6}{x - 20}$

⇒ $\dfrac{6}{x} = \dfrac{7x - 140 - 6x + 240}{(x - 40)(x - 20)}$

⇒ $\dfrac{6}{x} = \dfrac{x + 100}{{x}^{2} - 60x + 800}$

⇒ 6x²- 360x +4800 = x² + 100x

⇒ 6x² - x ² - 360x - 100x + 4800 = 0

⇒ 5x² - 460x + 4800 = 0

⇒ 5 ( x² - 92x + 960 ) = 0

⇒ x² -92x + 960 = 0

⇒ x² -80x -12x + 960 = 0

⇒ x( x - 80 ) - 12 ( x - 80 ) = 0

⇒( x - 80 )( x - 12 ) = 0

⇒ x - 80 = 0 ; x - 12 = 0

⇒ x = 80 ; x = 12

➠ x = 80 ; 12

Hence, x cannot be equal to 12 because if x = 12 then every kg of dal and that of rice will be negetive.

$\therefore$ Rehena purchased fish by Rs 80.

Answer 2

Answer:

Rehana purchased fish Rs. 80