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Q.

Vijay had some bananas and 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 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. What is the total number of bananas he had?


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a

350

b

400

c

500

d

450 

answer is C.

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Detailed Solution

Given, Vijay had some bananas and 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 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.
Let the number of bananas that Vijay had in two lots A and B are x and y respectively. According to the first condition we get,
2x 3 +1y=400 ⇒2x+3y=1200  .... 1   And, according to the second condition we get,
  1x+ 4y 5 =460 ⇒5x+4y=2300  .... 2  
On multiplying equation (1) by 4 and equation (2) by 3, we get,
8x+12y=4800    .... 3   And,
15x+12y=6900   .... 4  
On solving equations (3) and (4), we get,
8x+12y=4800 15x+12y=6900 −    −     − ¯ 7x=2100 ⇒x=300  
Now, we substitute x =300 in equation (1) to get the value of y.
⇒2 300 +3y=1200 ⇒3y=600 ⇒y=200   Thus, the total number of bananas he had was 200+300=500  .
Hence, the correct option is 3.
 
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Vijay had some bananas and 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 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. What is the total number of bananas he had?