Question

The average height of Sanchi and Aarav is 12P cm. The average height of Aarav, Charu and Deepika is 10P cm.The average height of Charu and Deepika is 8P cm. Find Sanchi's height in terms of P.

Answer 1

Hint: In order to solve this problem we will make the equations from the average of every person’s height and then we will calculate the height of Sanchi with the help of those equations. Those equations can be formed as per the given condition in the equation. Like the average of n numbers can be calculated as the sum of all the numbers divided by n.

Complete step-by-step answer:
Let the age of Sanchi, Arav, Charu and Deepika is S, A, C and D.
It is given that the average height of Sanchi and Aarav is 12P cm.
So, the equation can be formulated as:

$$\begin{gathered} {\displaystyle \frac{\text{S + A}}{\text{2}}}\text{ = 12P} \\ \text{S + A = 24P}..........\text{(1)} \end{gathered}$$
It is also given that the average height of Aarav, Charu and Deepika is 10P cm.
So, the equation can be formulated as:
$$\begin{gathered} {\displaystyle \frac{\text{D + C + A}}{3}}\text{ = 10P} \\ \text{A + D + C = 30P}..........\text{(2)} \end{gathered}$$
It is given that the average height of Charu and Deepika is 8P cm.
$$\begin{gathered} {\displaystyle \frac{\text{D + C}}{2}}\text{ = 8P} \\ \text{D + C = 16P}..........\text{(2)} \end{gathered}$$
On putting the value of D + C in the equation (2) we get,
A +16P = 30P.
A = 14P
On putting the value of A in equation (1) we get the value of S as:
14P + S = 24P
S = 10P
Hence the height of Sanchi is 10P.
So, the correct option is D.

Note: There are most of the questions at every level which are of this type in which students have to obtain the equation from the given question and solve those equations to get the value of the variables as an answer or the way to get the answer. Here students have to concentrate on algebra so that they get the value of each variable correct. This will help you to solve such types of problems.