Question

A: B = 2: 3
B : C = 5: 6
WHAT IS A: B: C

Answer 1

$\huge{\sf{\underline{\pink{Given:-}}}}$

A : B = 2 : 3

B : C = 5 : 6

$\huge{\sf{\underline{\blue{To\:find:-}}}}$

A : B : C

$\huge{\sf{\underline{\orange{Answer:-}}}}$

A : B = 2 : 3

⟶ $\frac{A}{B}$ = $\frac{2}{3}$

⟶ 3A = 2B--------------(i)

and

B : C = 5 : 6

⟶ $\frac{B}{C}$ = $\frac{5}{6}$

⟶ 6B = 5C---------------(ii)

WE NEED TO MAKE THE SECOND TERM OF (i) AND THE FIRST TERM OF (ii) EQUAL

$\sf{\underline{Multiply\:(i)\:with\:3}}$

ㅤ3A = 2B

ㅤㅤㅤ* 3

⟶ 9A = 6B

$\sf{From\:(ii)\:we\:know\:6B\:=\:5C}$

So we can say that,

9A = 6B = 5C

Therefore A : B : C

$\huge{\sf{\red{\boxed{\boxed{9\::6\::5}}}}}$