Question

Dan and Paul share some money in the ratio 9:5.
Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have?

Answer 1

Answer:

£40

Step-by-step explanation:

have a good day. thanks

Answer 2

Question :

Dan and Paul share some money in the ratio 9:5. Dan decides this is unfair so he gives Paul Rs. 32 of his share to make the ratio 1:1. How much money did Paul originally have?

Solution :

Let Dan have "M" number of money and Paul have "N" number of money.

• Dan and Paul share some money in the ratio 9:5.

According to question,

$\Rightarrow\:\dfrac{M}{N}\:=\:\dfrac{9}{5}$ _____ (eq 1)

$\Rightarrow\:M\:=\:\dfrac{9N}{5}$ _____ (eq 2)

• Dan decides to gives Rs. 32 to Paul and then the ratio becomes 1:1.

According to question,

$\Rightarrow\:\dfrac{M\:-\:32}{N}\:=\:\dfrac{1}{1}$

Cross multiply them

$\Rightarrow\:M\:-\:32\:=\:N$

$\Rightarrow\:\dfrac{9N}{5}\:-\:32\:=\:N$ [From (eq 2)]

$\Rightarrow\:\dfrac{9N\:-\:160}{5}\:=\:N$

$\Rightarrow\:9N\:-\:160\:=\:5N$

$\Rightarrow\:9N\:-\:5N\:=\:160$

$\Rightarrow\:4N\:=\:160$

$\Rightarrow\:N\:=\:40$

Put value of N in (eq 2)

$\Rightarrow\:M\:=\:\dfrac{9(40)}{5}$

$\Rightarrow\:M\:=\:72$

Paul have Rs. 40.

☆ Verification :

From above calculations we have M = 72 and N = 40

Put value of M and N in (eq 1)

$\Rightarrow\:\dfrac{72}{40}\:=\:\dfrac{9}{5}$

$\Rightarrow\:\dfrac{9}{5}\:=\:\dfrac{9}{5}$