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Ratio and Proportion

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Question : 108 of 112

Marks: +1, -0

The ratio of two numbers is

15: 19

. If a certain number is added to each term of the ratio it become 8: 9. What is the number added to each of the ratio?

6
15
17
23

Solution:

Concept:

Let the numbers be

15x

and

19x

. Adding

k

to both gives ratio

8:9

.

Explanation:

Set up the equation:

\frac{15x+k}{19x+k}=\frac{8}{9}

.

Cross-multiply:

9(15x+k)=8(19x+k)

.

Simplify:

135x+9k=152x+8k

.

Rearrange:

9k-8k=152x-135x

.

Thus

k=17x

.

Since

x

is a common factor, the simplest case is

x=1

.

Then

k=17

.

Answer:

The number added is

17

, which corresponds to option C.

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