Question

Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs. 1,00,000, how much money did Anima have?

Answer 1

Given :–

• Anima left ½ of her property to her daughter.
• And the ⅓ of her property to her son.
• The donation was worth Rs. 1,00,000.

To Find :–

• How much money did Anima have ?

Solution :–

Let,

• The donation worth be x.

in the given question,

The donated property is Rs. 1,00,000.

So, x = 1,00,000

• And the total property be y.

According to the problem,

She left ½ of her property to her daughter and ⅓ to her son.

So, the equation is,

→ $\dfrac{1}{2} y + \dfrac{1}{3} y + x = y$

→ $\dfrac{1}{2} y + \dfrac{1}{3} y - y = - x$

→ $\dfrac{y}{2} + \dfrac{y}{3} - \dfrac{y}{1} = - → x$

L.C.M. (least common multiple) of 2, 3 & 1 is 6

So,

→ $\dfrac{3y + 2y - 6y}{6} = - x$

→ $\dfrac{5y - 6y}{6} = - x$

→ $\dfrac{ - y}{6} = - x$

→ $6x = y$

Now, we have to find the value of y (total property),

Given that,

• x = Rs. 1,00,000

Now, put the value of x in equ. (1),

→ 6 × Rs. 1,00,000

→ Rs. 6,00,000

Hence,

Anima has Rs. 6,00,000.