a) 10 : 12 : 21

b) 5 : 7 : 13

c) 10 : 13 : 25

d) 11 : 12: 15

correct answer is : a) 10 : 12 : 21

Explanation

Here, A : B = 5 : 6
\therefore\ \frac{A}{B}\ =\ \frac{5}{6}
And, B : C = 4 : 7
\therefore\ \frac{B}{C}\ =\ \frac{4}{7}
So that,
\rightarrow\ \frac{A}{B}\ =\ \frac{5\ \times\ 4}{6\ \times\ 4}\ =\ \frac{20}{24}
\rightarrow\ \frac{B}{C}\ =\ \frac{4\ \times\ 6}{7\ \times\ 6}\ =\ \frac{24}{42} _{[make the B’s value same]}
\therefore\ A : B : C = 20 : 24 : 42
Or, A : B : C = 10 : 12 : 21 _{[convert simplest form]}
Ans: A : B : C = 10 : 12 : 21