Question

Ram had 14 mangoes and Raj had only 4 mangoes. Ram gave some mangoes to Raj and then Raj had exactly half the number of mangoes as Raj left with. Find the number of mangoes which Ram gave to Raj.

Answer 1

Hint – In this question let Ram give x mangoes to Raj. Construct a linear equation using the constraints given in the question. Solve the constructed equation to get the value of the variable x. The value of this variable will give the number of mangoes given by Ram to Raj.

Complete step-by-step answer:
Given data:
Ram had 14 mangoes
Raj had 4 mangoes.
Now let Ram give x mangoes to Raj.
So Ram has left with (14 – x) mangoes
And the mangoes Raj has become (4 + x).
Now it is given after the trade of mangoes Raj had exactly half the number of mangoes as Ram left with.
Now construct the linear equation according to given information we have,
Mangoes of Raj = half the mangoes of Ram
$ \Rightarrow \left( {4 + x} \right) = \dfrac{1}{2}\left( {14 - x} \right)$
Now simplify this we have,
$ \Rightarrow 8 + 2x = \left( {14 - x} \right)$
$ \Rightarrow 2x + x = 14 - 8$
$ \Rightarrow 3x = 6$
$ \Rightarrow x = \dfrac{6}{3} = 2$
So Ram gave 2 mangoes to Raj.
So this is the required answer.

Note – The key here was that when Ram gave some x mangoes so obviously now he will be having mangoes less than 14, so we reduce x numbers of mangoes form his overall lot of mangoes that is 14-x. Now as these mangoes that were taken from Ram are now given to Raj so Raj’s number of mangoes have now increased from 4 from 4+x. It works on the concept that the number of mangoes lost by one person is equal to the number of mangoes gained by another.