Question

Alvin and Simon shared £540 in the ratio 4:5. Alvin gave half of his share to Theo. Simon gave a tenth of his share to Theo. What fraction of the £540 did Theo receive.

Answer 1

Answer:

$\frac{5}{18}$

Step-by-step explanation:

sum the parts of the ratio, 4 + 5 = 9 parts

Divide the amount by 9 to find the value of one part of the ratio

£540 ÷ 9 = £60 ← value of 1 part of the ratio , thus

4 parts = 4 × £60 = £240 ← Alvin's share

5 parts = 5 × £60 = £300 ← Simon's share

$\frac{1}{2}$ × £240 = £120

$\frac{1}{10}$ × £300 = £30

Theo receives £120 + £30 = £150 , which as a fraction is

$\frac{150}{540}$ ( divide numerator/ denominator by 30 )

= $\frac{5}{18}$ ← in simplest form