Question

A and B each have a certain number of mangoes. A says to B “If you give me 30 of your mangoes, I will have twice as many as left with you”. B replies, “If you give me 10, I will have thrice as many as left with you”. How many mangoes does each have?

Answer 1

Hint: Assume the number of mangoes A is having as x and the number of mangoes B is having as y. Consider the two given situations and form two linear equations in variables x and y and solve them by the substitution method to get the answer.

Complete step-by-step answer:
Here, let us assume that A and B are having x and y number of mangoes respectively. Here, we have been given two situations, so let us check them one – by – one.
Condition 1: - In condition 1, it is said that if B gives his 30 mangoes to A then A will have twice the number of mangoes left with B. So, we have,
Number of mangoes with B = y
Number of mangoes left with B = y – 30
Number of mangoes with A = x
Number of mangoes with A after B gives 30 mangoes = x + 30
But the number of mangoes with A will be twice the number of mangoes left with B. Therefore, we have,
\[\begin{align}
  & \Rightarrow x+30=2\left( y-30 \right) \\
 & \Rightarrow x+30=2y-60 \\
\end{align}\]
\[\Rightarrow 2y-x=90\] - (1)
Condition 2: - In condition 2, it is said that if A gives his 10 mangoes to B then B will have thrice the number of mangoes left with A. So, we have,
Number of mangoes with A = x
Number of mangoes left with A = x – 10
Number of mangoes with B = y
Number of mangoes with B after A gives 10 mangoes = y + 10
But the number of mangoes with B will be thrice the number of mangoes left with A. Therefore, we have,
\[\begin{align}
  & \Rightarrow y+10=3\left( x-10 \right) \\
 & \Rightarrow y+10=3x-30 \\
\end{align}\]
\[\Rightarrow y=3x-40\] - (2)
Now, substituting the value of y from equation (2) in equation (1), we get,
\[\begin{align}
  & \Rightarrow 2\left( 3x-40 \right)-x=90 \\
 & \Rightarrow 6x-80-x=90 \\
 & \Rightarrow 5x=170 \\
 & \Rightarrow x=34 \\
\end{align}\]
Therefore, substituting the value of x in equation (2), we get,
\[\begin{align}
  & \Rightarrow y=3\times 34-40 \\
 & \Rightarrow y=102-40 \\
 & \Rightarrow y=62 \\
\end{align}\]
Hence, the number of mangoes with A and B are 34 and 62 respectively.

Note: One may note that we must read the question carefully otherwise we will get confused in the language of the question. We have assumed two variables x and y because we were supposed to find the number of mangoes contained by two persons, A and B. We cannot solve this question by considering only one variable. You may see that here we have used the substitution method to solve the two equations but you may use the elimination method or the method of cross – multiplication. The answer will be the answer.