Question

A father wants to divide Rs 200 into two parts between two sons such that by adding three times the smaller part to half of the larger part then its will always be less than Rs 200. How will he divided this amount?​

Answer 1

Given as :

The sum of money to be divided between two parts = Rs 200

Adding three times the smaller part to half of the larger part then its will always be less than Rs 200

To Find :

How will amount is divided

Solution :

Let The smaller part = Rs S

The larger part = Rs L

∵  The sum of parts = Rs 200

Or,   Larger + Smaller = Rs 200

Or.  L + S = Rs 200                ..............1

And

Adding three times the smaller part to half of the larger part then its will always be less than Rs 200

i.e   ( 3 S + $\dfrac{1}{2}$ × L ) - 200 = 0

Or,   3 S + $\dfrac{L}{2}$  = 200                    

Or,  6 S + L = 400                         ...........2

Solving eq 1 and eq 2

    (  6 S + L ) - (  L + S ) = 400 - 200

Or,  ( 6 S - S ) + ( L - L ) = 200

Or,   5 S + 0 = 200

i.e    S = $\dfrac{200}{5}$

∴  Smaller = S = Rs 40

Now, Put the value of S into eq 1

L + S = Rs 200

Or,  L + Rs 40 = Rs 200

Or,   L = 200 - 40

i.e    L = Rs 160

Larger = L = Rs 160

Hence, The Larger part is Rs 160

And The Smaller part is Rs 40         . Answer