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WAEC Mathematics 2023 Paper

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Question : 21

Total: 50

m:n =

2\frac{1}{3} : 1\frac{1}{5}

1\frac{1}{2} : 1\frac{1}{3}

, find q : m.

35 : 18
16 : 35
18 : 35
35 : 16

Solution:

Concept:

Ratios are compared by converting each pair into fractional form and then eliminating the common term.

Explanation:

Write

m:n

as fractions:

2\frac13=\frac73

and

1\frac15=\frac65

.

So

\frac{m}{n} = \frac73 \div \frac65 = \frac73 \times \frac56 = \frac{35}{18}

.

Thus

m = \frac{35n}{18}

.

Next, write

n:q

as fractions:

1\frac12=\frac32

and

1\frac13=\frac43

.

So

\frac{n}{q} = \frac32 \div \frac43 = \frac32 \times \frac34 = \frac98

.

Thus

q = \frac{8n}{9}

.

Now find

q:m

, which is

\frac{q}{m} = \frac{8n}{9} \div \frac{35n}{18}

.

This simplifies to

\frac{8n}{9} \times \frac{18}{35n} = \frac{16}{35}

.

Therefore,

q:m = 16:35

.

Answer:

q:m = 16:35

(Option B).

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