Test Index

Ratio and Proportion

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Question : 58 of 112

Marks: +1, -0

If

a: b=c: d=3: 5,

then what are the values of ad: bc is

$3: 5$
$5:3$
$1: 1$
None

Solution:

Concept:

When two ratios are equal, their cross products are equal.

Here, both

a:b

and

c:d

are equal to

3:5

, implying

ad = bc

.

Explanation:

Given

a:b = 3:5

and

c:d = 3:5

.

This means

\frac{a}{b} = \frac{3}{5}

and

\frac{c}{d} = \frac{3}{5}

.

So we can write

a = \frac{3}{5} b

and

c = \frac{3}{5} d

.

Now compute

ad

:

ad = \left(\frac{3}{5} b\right) \cdot d = \frac{3}{5} (bd)

.

Compute

bc

:

bc = b \cdot \left(\frac{3}{5} d\right) = \frac{3}{5} (bd)

.

Thus

ad = bc

.

Therefore, the ratio

ad : bc

simplifies to

1:1

(since equal quantities are in the ratio

1:1

).

Answer:

1:1

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