Question

. If a:b=5:6 and b:c=9:11, find the values of a, b and c.

Answer 1

Answer: a=45, b=63, c=66

Step-by-step explanation:

Given:

• a:b = 5:6

• b:c = 9:11

To find :

Values of a,b and c

Solution:

Here, all we have to do is equalise the term 'b' in both the ratios by multiplying it by the suitable factors.

a : b = 5 : 6

b : c = 9 : 11

Here, the LCM of the term 'b' in both the ratios is 63 (6×9=63) which means

We will multiply the first ratio by 9 and the second ratio by 6.

a : b = (5×9) : (6×9) = 45 : 63

a : b = (5×9) : (6×9) = 45 : 63b : c = (9×6) : (11×6) = 63 : 66

$\implies \boxed{a:b:c=45:63:66}$

Hence, a = 45, b = 63 , c = 66

Answer 2

Answer: a = 45, b = 63, c = 66

Step-by-step explanation:

It is given that

a:b = 5:6  and

b:c = 9:11

So to find a, b and c, by making the term 'b' in both the ratios by multiplying it by factors equal.

a : b = 5 : 6

b : c = 9 : 11

Here, the LCM of the term 'b' in both the ratios is 6×9=63 in which we will multiply the first ratio by 9 and the second ratio by 6.

a : b = (5×9) : (6×9) = 45 : 63

a : b = (5×9) : (6×9) = 45 : 63b : c = (9×6) : (11×6) = 63 : 66

We can also solve them by converting them them to fractions. Converting ratios to fractions is easy - a

                                           ----

                                             b

So, we can say that a = 45, b = 63, c = 66