Question

Sushil and Fiona win some money and share it in the ratio 4:1. Sushil gets £33 more than Fiona. How much did they get altogether?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Total\:prize\:money=\pounds55}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Ratio \: of \: their \: share = 4 : 1 \\ \\ \tt: \implies Sushil \: gets \: \pounds 33 \: more \: tha \: Fiona \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Total\:prize \: money = ?$

• According to given question :

$\circ \: \text{Let \: money \:get\: Fiona \: be \: \pounds x } \\ \\ \circ \: \text{Sushil \:get\: \pounds(33 + x) }\\ \\ \bold{As \: according \: to \: given \: Ratio} \\ \tt: \implies {Sushil \: money} : {Fiona \: money} = 4 : 1 \\ \\ \tt: \implies \frac{Sushil \: money}{Fiona \: money} = \frac{4}{1} \\ \\ \tt: \implies \frac{33 + x}{x} = \frac{4}{1} \\ \\ \tt: \implies 33 + x = 4x \\ \\ \tt: \implies 33 = 4x - x \\ \\ \tt: \implies 3x = 33 \\ \\ \tt: \implies x = \frac{33}{3} \\ \\ \green{\tt: \implies x = \pounds11} \\ \\ \green{\tt\therefore Fiona \: get \: \: \pounds11} \\ \\ \green{\tt\therefore Sushil \: get\: \: \pounds44} \\ \\ \green{\tt\therefore Total \: prize \: money = \pounds55}$

Answer 2

Step-by-step explanation:

Let the money Sushil has be x.

And money with Fiona be y.

Given ratio =4:1.

Therefore, by cross multiplication

$\frac{x}{y} = \frac{4}{1}$

$x = 4y$

Now According to the question,

Sushil =33+Fiona

x=33+y

x-y= 33

Now by putting the value of x, we get

4y-y =33

3y = 33

y = 11

And,

x-11=33

x = 33+11=44.

Therefore, Sushil has £11 and Fiona has £44, and the total amount they have is £55.