In an office, \;2/3 of the telephone bill is paid by Tom, \;1/5 by Azuma and the remaining by Tina. What fraction is paid by Tina?

Correct Answer is : 215\;2/15152

In an office, \;2/3 of the telephone bill is paid by Tom, \;1/5 by Azuma and the remaining by Tina. What fraction is paid by Tina?

Correct Answer is : 215\;2/15152

Test Index

BECE Mathematics 2013 Paper

Question : 31

Total: 40

In an office,

\;\frac{2}{3}

of the telephone bill is paid by Tom,

\;\frac{1}{5}

by Azuma and the remaining by Tina. What fraction is paid by Tina?

$\;\frac{2}{15}$
$\;\frac{1}{4}$
$\;\frac{1}{3}$
$\;\frac{7}{15}$

Validate

Solution:

Concept:

The entire telephone bill is taken as one whole unit. The fraction paid by Tina is the remaining part after subtracting the fractions paid by Tom and Azuma from the whole.

Explanation:

First, add the fractions paid by Tom and Azuma.

Tom's share

= \frac{2}{3}

and Azuma's share

= \frac{1}{5}

So, total paid by both

= \frac{2}{3} + \frac{1}{5}

Convert to a common denominator, which is

15

\frac{2}{3} = \frac{10}{15}

and

\frac{1}{5} = \frac{3}{15}

Therefore,

\frac{2}{3} + \frac{1}{5} = \frac{10}{15} + \frac{3}{15} = \frac{13}{15}

Now, the whole bill is

1 = \frac{15}{15}

The remaining fraction paid by Tina is obtained by subtracting the total paid by Tom and Azuma from the whole bill.

Tina's share

= 1 - \frac{13}{15} = \frac{15}{15} - \frac{13}{15} = \frac{2}{15}

Hence, Tina pays

\frac{2}{15}

of the telephone bill.

Answer:

\frac{2}{15}

, which is Option A.

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