Question

There are some apples in two boxes B1 and B2. If two apples are added to B2 from B1, the number of apples in each box will be equal. If two apples from B2 are added to B1, the number of apples in B1 would be double that of B2. Find the initial number of apples in B1 and B2 respectively. O 14,15 o 14, 12 O 14,10 O 13, 12​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

Number of apples in box B1 be x

and

Number of apples in box B2 be y

According to first condition

If two apples are added to B2 from B1, the number of apples in each box will be equal.

So,

Number of apples in box B1 = x - 2

and

Number of apples in box B2 = y + 2

Thus,

$\rm :\longmapsto\:x - 2 = y + 2$

$\rm :\longmapsto\:x - y = 4 - - - (1)$

According to second condition

If two apples from B2 are added to B1, the number of apples in B1 would be double that of B2

So,

Number of apples in box B1 = x + 2

and

Number of apples in box B2 = y - 2

Thus,

$\rm :\longmapsto\:x + 2 = 2(y - 2)$

$\rm :\longmapsto\:x + 2 = 2y - 4$

$\rm :\longmapsto\:x - 2y= - 6 - - - - (2)$

On Subtracting equation (2) from equation (1), we get

$\rm :\longmapsto\:(x - y) - (x - 2y) = 4 - ( - 6)$

$\rm :\longmapsto\:x - y- x + 2y = 4 + 6$

$\bf\implies \:y = 10$

On substituting y = 10 in equation (1), we get

$\rm :\longmapsto\:x - 10 = 4$

$\bf\implies \:x = 14$

Hence,

Number of apples in box B1 = 14

and

Number of apples in box B2 = 10

Answer 2

Given: Two boxes B1 and B2 have some apples, If two apples are added to B2 from B1, the number of apples in each box will be equal. If two apples from B2 are added to B1, the number of apples in B1 would be double that of B2.

To find: Find the initial number of apples in B1 and B2 respectively.

Solution:

Assume that the number of apples in box B1 is x and the number of apples in box B2 is y.

Know that from the question, two apples are added to B2 from B1, the number of apples in each box will be equal.

Form the required equation and solve it.

$\[\begin{array}{l}x - 2 = y + 2\\ \Rightarrow x - y = 4 - - - - - - \left( 1 \right)\end{array}\]$

Observe that from the given question that,  If two apples from B2 are added to B1, the number of apples in B1 would be double that of B2.

Form the required equation and solve it.

$\[\begin{array}{l}x + 2 = 2\left( {y - 2} \right)\\ \Rightarrow x + 2 = 2y - 4\\ \Rightarrow x - 2y = - 4 - 2\\ \Rightarrow x - 2y = - 6 - - - - - - \left( 2 \right)\end{array}\]$

$\[\begin{array}{l}x - y = 4\\ \Rightarrow x = 4 + y - - - - - - - \left( 3 \right)\end{array}\]$

Solve equations (3) and (2).

$\[\begin{array}{l}x - 2y = - 6\\ \Rightarrow \left( {4 + y} \right) - 2y = - 6\\ \Rightarrow 4 - y = - 6\\ \Rightarrow y = 10\end{array}\]$

Find the value of x.

$\[\begin{array}{l}x = 4 + y\\ \Rightarrow x = 4 + 10\\ \Rightarrow x = 14\end{array}\]$

Hence,  the initial number of apples in B1 and B2 are $14$ and $10$ respectively.