WAEC 2010 · Paper 2 · Q1

(a)
Two children shared an amount of money in the ratio $\frac34 : \frac25$ . If the smaller share was GH¢25.00, how much was shared between them?
(b)
A box contains 5 red, 3 green and 4 blue balls of the same size. If a boy picks two balls from the box one after the other without replacement, what is the probability that both balls are red?

Worked solution (try it first)

(a)

Clear the fractions: multiply both parts of $\frac34 : \frac25$ by 20 (the LCM of 4 and 5) to get $15 : 8$ .
The ratio has $15 + 8 = 23$ parts, and the smaller share is 8 of them.
So $\frac{8}{23}$ of the amount is GH¢25.00, and the amount is $25 \times \frac{23}{8} = 71.875$ .
They shared GH¢71.88 (to the nearest pesewa).

(b)

There are $5 + 3 + 4 = 12$ balls.
The first ball is red with probability $\frac{5}{12}$ .
One red ball has gone, so the second is red with probability $\frac{4}{11}$ .
Multiply: $\frac{5}{12} \times \frac{4}{11} = \frac{20}{132}$
$= \frac{5}{33}$ .

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