Question

What is the least integer which when added to both terms of the ratio 5:9 will make a ratio grrater than 7:10?

Answer 1

Let x be the least integer added to both terms of the ratio 5 : 9

Then we get (5 + x) / (9 + x)

According to the question

(5 + x) / (9 + x) > 7/10

by cross multiplication

10(5 + x) > 7(9 + x)

50 + 10x > 63 + 7x

10x - 7x > 63 - 50

3x > 13

x > 13/3

x > 4 1/3(mixed fraction )

Therefore, the least integer required is 5

Answer 2

Ratio of two terms = 5 : 9

Let the least number be x

x is added to the both the terms

=> (5 + x), (9 + x)

Ratio after the least term is added = 7 : 10

Acording to the question :

(5 + x)/(9 + x) = 7/10

By Cross Multiplication :

(5 + x)10 = 7(9 + x)

50 + 10x = 63 + 7x

10x - 7x = 63 - 50

3x = 13

x = 13/3

Therefore the least integer is 13/3.