Question

The sum of the heights A and B is $320$ cm and the difference of the heights A and B is
$20$cm. The height of B can be
(a). $140cm$
(b). $145cm$
(c). $150cm$
(d). $155cm$

Answer 1

Hint: In this question we will use the sum and difference of the heights of A and B given in the question to generate the equations and then solve for the unknown, that is, to find the height of B.

Complete step by step solution:
Sum of the heights A and B is $320$cm and the difference of the heights A and B is $20$cm.

Let height of A is x cm and the height of B is y cm.
sum of the heights A and B is $320$cm (given in the question)
Now, we can generate the equation using sum of the heights A and B is $320$cm as:
$x + y = 320$
$x = 320 - y$………..(1)(let us consider this as equation 1)
Difference of the heights of A and B is $20$cm
we can generate the equation using difference of the heights A and B is $20$cm as
$x - y = 20$………….(2)(let us consider this as equation 2)
By putting the value of $x = 320 - y$ from equation (1) in equation (2), we will get:
$320 - y - y = 20$
$320 - 2y = 20$
$2y = 320 - 20$
$2y = 300$
$y = \frac{{300}}{2} = 150$

Hence, the height of B can be $150$cm. Option (c) is the correct answer.

Note: If sum and difference of two quantities are given then we can find the value of the individual quantity by making the equations and solving it for the unknown value.