Question

The sum of three numbers is $192$. If the ratio of first number to the second number is $3:5$ and that of second number to the third number is $7:8$, then find the first number.

Answer 1

Step $1:$Finding the ratio of first, second and third number:

To find ratio of first, second and third number, we have to make second number equal in both the ratios then combine them.

$$\begin{gathered} \text{First Number:Second Number=3:5=}\frac{3}{5} \\ \mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numbers}\mathrm{by}7 \\ \frac{3}{5}=\frac{3\times 7}{5\times 7}=\frac{21}{35} \end{gathered}$$ $$\begin{gathered} \text{Second Number:Third Number=7:8=}\frac{7}{8} \\ \mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numbers}\mathrm{by}5 \\ \frac{7}{8}=\frac{7\times 5}{7\times 5}=\frac{35}{40} \end{gathered}$$

Therefore, $\text{First Number:Second Number:Third Number=21:35:40}$

Step $2:$ Finding the first number:

Let the first, second and third number be $\text{21x, 35x, 40x}$ respectively.

Sum of the three numbers $\text{=21x+35x+40x=96x}$

According to question, sum of three numbers is $192$

$$\begin{gathered} \text{⇒96x=192} \\ \text{⇒ x=}\frac{192}{96} \\ \Rightarrow x=2 \end{gathered}$$

Therefore, the first number is $\text{=21x=21×2=42}$.