Experts please help ....
question - Raju was fascinated by a new car and he wanted to buy it but he did not have enough money.His father offered him 1/2 of the price.And so his mother offered 1/2 of the remaining.His brother also offered half of the remaining .His sisteroffered the other half of of remaining .And his friend also gave half of the remaining. Hefound that he had with him RS20,000 and now he had just enough money to buy the car with all help of his family and friends.what is the cost of the car ?

Answer :

Let price of Car  =  x 

And given : His father offered him $\frac{1}{2}$ of the price , So
His father gave him total money for car  = $\frac{x}{2}$
So,
Remaining amount  =  x  - $\frac{x}{2}$  =  $\frac{x}{2}$ 
And ,  his mother offered $\frac{1}{2}$ of the remaining , So
His mother offered total money for car  = $\frac{x}{4}$ 
And
Remaining amount  =  x  - ( $\frac{x}{2}$ + $\frac{x}{4}$   )   = x  -  $\frac{3 x}{4}$  = $\frac{x}{4}$ 
And ,  his brother offered $\frac{1}{2}$ of the remaining , So
His brother offered total money for car  = $\frac{x}{8}$ 
And
Remaining amount  =  x  - ( $\frac{x}{2}$ + $\frac{x}{4}$  + $\frac{x}{8}$  )   = x  -  $\frac{7 x}{8}$  =$\frac{x}{8}$ 
And ,  his sister offered $\frac{1}{2}$ of the remaining , So
His sister offered total money for car  = $\frac{x}{16}$    

And
Remaining amount  =  x  - ( $\frac{x}{2}$ + $\frac{x}{4}$  + $\frac{x}{8}$ + $\frac{x}{16}$  )   = x  -  $\frac{15 x}{16}$  = $\frac{x}{16}$ 
And ,  his friend offered $\frac{1}{2}$ of the remaining , So
His friend offered total money for car  =   $\frac{x}{32}$

And also given He found that he had with him Rs. 20,000 and now he had just enough money to buy the car with all help of his family and friends.
So,
Money offered by father + Money offered by mother + Money offered by brother + Money offered by sister + Money offered by friend =  20000 , So

$\frac{x}{2}$  + $\frac{x}{4}$ + $\frac{x}{8}$ +  $\frac{x}{16}$  + $\frac{x}{32}$  =  20000
Taking L.C.M. we get

$$\begin{gathered} \Rightarrow \frac{16x + 8x + 4x + 2x + x}{32} = 20000 \\ \Rightarrow 16x + 8x + 4x + 2x + x = 640000 \\ \Rightarrow 31x = 640000 \\ \Rightarrow x =\frac{ 640000}{31} \\ \Rightarrow x =20645.16 \end{gathered}$$
So,
We can say price of car nearly  =  Rs. 20645                                ( Ans )