Vijay had some bananas,and he divided them in | vedclass

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(A) Let the number of bananas in lots $A$ and $B$ be $x$ and $y$,respectively.Case $I$: Cost of the first lot at the rate of $Rs. 2$ for $3$ bananas $

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$500$

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(A) Let the number of bananas in lots $A$ and $B$ be $x$ and $y$,respectively.Case $I$: Cost of the first lot at the rate of $Rs. 2$ for $3$ bananas $+$ cost of the second lot at the rate of $Rs. 1$ per banana $=$ amount received.$\frac{2}{3}x + y = 400$$2x + 3y = 1200 \dots (i)$Case $II$: Cost of the first lot at the rate of $Rs. 1$ per banana $+$ cost of the second lot at the rate of $Rs. 4$ for $5$ bananas $=$ amount received.$x + \frac{4}{5}y = 460$$5x + 4y = 2300 \dots (ii)$On multiplying Eq. $(i)$ by $4$ and Eq. $(ii)$ by $3$,we get:$8x + 12y = 4800$$15x + 12y = 6900$Subtracting the first from the second:$(15x - 8x) + (12y - 12y) = 6900 - 4800$$7x = 2100$$x = 300$Now,substitute the value of $x$ in Eq. $(i)$:$2(300) + 3y = 1200$$600 + 3y = 1200$$3y = 600$$y = 200$Total number of bananas $= x + y = 300 + 200 = 500$.

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