Question

if A:B=2:3,B:C=5:6 find AC​

Answer 1

$\sf{Answer}$

Given :-

• Ratio of A: B = 2 :3
• B :C = 5 :6

To find :-

• A:C value

Solution :-

In A : B and B :C "B" is common So, LCM of 3, 5 is 15

Multiply A : B with 5

Multiply B : C with 3

A : B = (2 : 3) 5

A : B = 10 : 15

B : C = ( 5: 6 ) 3

B : C = 15 : 18

Now , the ratio of B is same

A : B : B : C = 10 : 15 : 15 : 18

A : B : C = 10 : 15 : 18

A :C = 10:18 We can simplify

A : C = 5 : 9

So, ratio of A: C IS 5:9

Answer 2

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• A : B = 2:3
• B : C = 5:6

$\underline{\underline{\sf{\maltese\:\:To\: Find}}}$

• value of A : C

$\underline{\underline{\sf{\maltese\:Calculations \:}}}$

So firstly we can say that :-

$\longrightarrow \: \frac{a}{b} = \frac{2}{3}$

$\longrightarrow \: \frac{1}{b} \: = \frac{2}{3a}$

Thus,

$\longrightarrow \: \purple{b = \frac{3a}{2} } \: \: \: \: \: \: \: ..eq(1)$

Now, as given :-

$\longrightarrow \: \frac{b}{c} = \frac{5}{6}$

Thus,

$\longrightarrow \: \pink{b = \frac{5c}{6} }\: \: \: \: \: \: \: ..eq(2)$

Now comparing both the equation with LHS being 'B'

Therefore,

$\longrightarrow \: \frac{3a}{2} = \frac{5c}{6}$

$\longrightarrow \: \frac{3a}{ \cancel2} = \frac{5c}{ \cancel6}$

$\longrightarrow \: {3a} = \frac{5c}{3}$

by cross multiplying, we get :-

$\longrightarrow \: a = \frac{5c}{9}$

$\longrightarrow \: \red{ \frac{a}{c} = \frac{5}{9}}$

Hence, the value of A : C is 5 : 9.