Test Index

Ratio and Proportion

Question : 27 of 112

Marks: +1, -0

3 : 4

. The first part is

Solution:

Concept:

Let the first part be

x

, so the second part is

94 - x

, and form an equation from the given ratio of their fractions.

Explanation:

Let the first part be

x

Then the second part is

94 - x

The fifth part of the first is

\frac{x}{5}

The eighth part of the second is

\frac{94 - x}{8}

Their ratio is

3 : 4

, so:

\frac{\frac{x}{5}}{\frac{94 - x}{8}} = \frac{3}{4}

Simplify:

\frac{x}{5} \times \frac{8}{94 - x} = \frac{3}{4}

\frac{8x}{5(94 - x)} = \frac{3}{4}

Cross multiply:

4 \times 8x = 3 \times 5(94 - x)

32x = 15(94 - x)

32x = 1410 - 15x

32x + 15x = 1410

47x = 1410

x = \frac{1410}{47} = 30

Thus, the first part is 30.

Answer:

The first part is 30.

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