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Sequence and Series

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Question : 34 of 86

Marks: +1, -0

The ratio of the sum and the difference of two numbers is

7: 1 .

Find the ratio of those two numbers.

$5: 3$
$4: 3$
$4: 5$
None

Solution:

Concept:

Let the two numbers be

a

and

b

. The given ratio of their sum to difference is

7 : 1

.

Explanation:

We have

\frac{a+b}{a-b} = \frac{7}{1}

.

Cross-multiplying:

a+b = 7(a-b)

.

Expand:

a+b = 7a - 7b

.

Bring like terms:

b + 7b = 7a - a

.

So

8b = 6a

.

Thus

\frac{a}{b} = \frac{8}{6} = \frac{4}{3}

.

Hence the ratio

a : b = 4 : 3

.

Answer:

The ratio is

4 : 3

, which corresponds to option B.

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