Question

1.      P, Q and R were sharing profits in the ratio of 8:5:3. P retired and Q took 1/6 of P’s share and R took 5/6th of his share. New profit-sharing ratio will be​

Answer 1

Answer:

New profit-sharing ratio will be 19 : 29

Step-by-Step Explanation:

Profit sharing ratio of P,Q and R = 8 : 5 : 3

So,

P's share of profit = $\sf{\frac{8}{16}}$

Q's share of profit = $\sf{\frac{5}{16}}$

R's share of profit = $\sf{\frac{3}{16}}$

P retired and Q took $\sf{\frac{1}{6}}$th of P’s share and R took $\sf{\frac{5}{6}}$ th of his share

So,

Share taken by Q =

$\longrightarrow$$\sf{\dfrac{8}{16} \times \dfrac{1}{6}}$

$\longrightarrow$$\sf{\dfrac{8}{96}}$

$\rule{300}{1.5}$

Share taken by R =

$\longrightarrow$$\sf{\dfrac{8}{16} \times \dfrac{5}{6}}$

$\longrightarrow$$\sf{\dfrac{40}{96}}$

$\rule{300}{1.5}$

Q's new Share =

$\longrightarrow$$\sf{\dfrac{5}{16} + \dfrac{8}{96} = \dfrac{38}{96}}$

$\rule{300}{1.5}$

R's new Share =

$\longrightarrow$$\sf{\dfrac{3}{16} + \dfrac{40}{96} = \dfrac{58}{96}}$

$\rule{300}{1.5}$

Q's share : R's share

$\longrightarrow$$\sf{\dfrac{38}{96} : \dfrac{58}{96}}$

$\longrightarrow$ $\sf{\dfrac{19}{48} : \dfrac{29}{48}}$

19 : 29

Therefore,

New profit-sharing ratio will be 19 : 29