Question

Divide Rs. 7000 among A, B, C such that A gets $$50\% $$ of what B get $$50\% $$ of what C get. Find the share of each person?

Answer 1

Hint: Here the given question is a word problem, we have to find the shares of persons A, B and C. For this, first we need to consider a share of person C be x then by the given data take share of B be $$\dfrac{x}{2}$$ and share of A be $$\dfrac{x}{4}$$ on next add the shares of all 3 persons ad equate with total amount i.e., 7000 on further simplification we get the required solution.

Complete step-by-step solution:
Consider a given question:
The total amount to be divide $$ = 7000$$
Let us consider the share of person C to be ‘$$x$$’ .
Given, B gets shares $$50\% $$ of C$$ = \dfrac{x}{2}$$.
A gets shares $$50\% $$ of B $$ = \dfrac{1}{2} \times \dfrac{x}{2} = \dfrac{x}{4}$$.
We have to find the shares of each person's A, B and C.
now, Rs. of A + Rs. of B + Rs. of C = Rs. 7000
$$ \Rightarrow \,\,\,x + \dfrac{x}{2} + \dfrac{x}{4} = 7000$$
Take 4 as LCM in LHS, then we have
$$ \Rightarrow \,\,\,\dfrac{{4x + 2x + x}}{4} = 7000$$
$$ \Rightarrow \,\,\,\dfrac{{7x}}{4} = 7000$$
Multiply both sides by 4
$$ \Rightarrow \,\,\,7x = 7000 \times 4$$
$$ \Rightarrow \,\,\,7x = 28000$$
Divide both sides by 7
$$ \Rightarrow \,\,\,x = \dfrac{{28000}}{7}$$
On simplification, we get
$$\therefore \,\,\,x = 4000$$
Therefore, C gets $$RS.\,\,4000$$
B get’s $$\dfrac{{4000}}{2} = RS.\,\,2000$$
A gets $$\dfrac{{4000}}{4} = RS.\,\,1000$$.
Hence, it’s a required solution.

Note: In a word problem read carefully each sentence it has information about the given problem that is how we are going to solve it and note down the data’s step by step of each sentence. The selection of mathematical methods will be dependent on each sentence so we have to choose an appropriate method while solving.
Remember $$50\% $$ represents a half of the quantity.