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Common Information

$P$ divides his property among his four sons $A, B, C$ and $D$ after donating Rs 20,000 and $10\%$ of his remaining property. The amounts received by the last three sons are in $A.P.$ and the amount received by the fourth son is equal to the total amount donated.

The first son receives as his share Rs 20,000 more than the share of the second son. The last son received Rs 1 lakh less than the eldest son.


Common Information Question: 2/2

Find the share of the third son.


Rs 80,000


Rs 1,00,000


Rs 1,20,000


Rs 1,50,000

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Option(C) is correct

All amounts are in thousands of rupees.

Let $P$'s total property be $(20+10p)$

The donation is $20+p$

The $4^{th}$ son's share is $20+p$

The $1^{st}$ son's share is $120+p$

The $2^{nd}$ son's share is $100+p$

The $3^{rd}$ son's share is $60+p$

As, $4^{th},3^{rd}$ and $2^{nd}$ are in $AP$

Thus, $300+4p=9p$

$\Rightarrow  p=60$

The 3rd son's share is $60+p= 120,000$

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