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Solving a Quadratic Equation by Factorization Method

Vijay had som...

Question

Vijay had some bananas , and he divided them into two lots A and B . He sold first lot at the rate of ₹2 for 3 bananas and the second lot at the rate of ₹1 per banana and got a total of ₹400 . If he had sold the first lot at the rate of ₹1 per banana and the second lot at the rate of ₹4 per five bananas, his total collection would have been ₹460 . Find the total number of bananas he had .

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Solution

Let the bananas in lot A be x and that in lot B be y.
Vijay sold 3 bananas for Rs 2 in lot A.
So, the cost of x bananas in lot A = $\frac{2}{3} x$
Now,
Cost of x bananas in lot A + Cost of y bananas in lot B = ₹400
$∴ \frac{2}{3} x + y = 400$
⇒ 2x + 3y = 1200 .....(i)
Now, if he sells the first lot at the rate of Rs 1 per banana and second for Rs 4 for 5 bananas, then
$x + \frac{4}{5} y$ = ₹460
⇒ 5x + 4y = 2300 .....(ii)
Solving (i) and (ii), we get
x = 300 and y = 200
So, the total number of bananas = x + y = 300 + 200 = 500.

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Q. Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of Rs 2 for 3 bananas and the second lot at the rate of Re 1 per banana and got a total of Rs 400. If he had sold the first lot at the rate of Re 1 per banana and the second lot at the rate of Rs 4 for 5 bananas, his total collection would have been Rs 460. Find the total number of bananas he had.

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राम के पास कुछ संतरें हैं तथा वह इन्हें दो भागों A व B में विभाजित करता है। वह प्रथम भाग A को ₹ 4 प्रति 6 संतरों की दर से तथा भाग B को ₹ 2 प्रति संतरे की दर से बेचता है तथा कुल ₹ 1200 प्राप्त करता है। यदि उसने प्रथम भाग A को ₹ 2 प्रति संतरे की दर से तथा द्वितीय भाग B को ₹ 8 प्रति 10 संतरों की दर से बेचा होता, तब उसे कुल ₹ 1000 प्राप्त होते, तब उसके पास कुल कितने संतरे थे?

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per orange. He also buys an equal number of bananas at the rate of Rs.

2

per banana. He makes a

20

% profit on orange and

15

% profit on bananas. At the end of the day, all the fruit is sold out. His total profit is Rs.

390

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