A man has divided his total money in his will in such a way that half

1.	A man has divided his total money in his will in such a way that half of it goes to his wife, \(\frac23\) rd of the remaining among his three sons equally and the rest among his four daughters equally. If each daughter gets Rs 20,000, how much money will each son get ?
Answer» Let the total money, the man had = Rs x Money gone to wife = Rs \(\frac{x}2\) Remaining money = \(\frac{x}2\) ∴ Sons' share = \(\frac23\) of \(\frac{x}2\) = Rs \(\frac{x}3\) Each son's share = \(\frac13\) of Rs\(\frac{x}3\) = Rs \(\frac{x}9\) Daughters' share = \(\frac{x}2\) - \(\frac{x}3\) = \(\frac{x}6\) Each daughter's share = \(\frac14\) x Rs \(\frac{x}6\) Rs \(\frac{x}{24}\) Given, \(\frac{x}{24}\) = 20000 ⇒ x = Rs 480000 ∴ Each son's share = \(\frac{480000}{9}\) = Rs 53,333.33

A man has divided his total money in his will in such a way that half of it goes to his wife, \(\frac23\) rd of the remaining among his three sons equally and the rest among his four daughters equally. If each daughter gets Rs 20,000, how much money will each son get ?

Answer»

Let the total money, the man had = Rs x

Money gone to wife = Rs \(\frac{x}2\)

Remaining money = \(\frac{x}2\)

∴ Sons' share = \(\frac23\) of \(\frac{x}2\) = Rs \(\frac{x}3\)

Each son's share = \(\frac13\) of Rs\(\frac{x}3\) = Rs \(\frac{x}9\)

Daughters' share = \(\frac{x}2\) - \(\frac{x}3\) = \(\frac{x}6\)

Each daughter's share = \(\frac14\) x Rs \(\frac{x}6\) Rs \(\frac{x}{24}\)

Given, \(\frac{x}{24}\) = 20000 ⇒ x = Rs 480000

∴ Each son's share = \(\frac{480000}{9}\) = Rs 53,333.33