Two numbers are in the ratio 5:7. If they differ by 42, find the great

1.	Two numbers are in the ratio 5:7. If they differ by 42, find the greater number?
Answer» ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ ★Question : ➊ Two numbers are in the RATIO 5:7 . If they differ by 42 , find the greatest NUMBER? ✯ To find: ➡ Greatest number =? ✮ Solution : ➜ Let x and y be the required two numbers where y > x. $\\ \therefore \sf \: the \: ratio \: \frac{x}{y} = \frac{5}{7} \implies \: \boxed { \sf{x = \frac{5y}{7} }} \to \: (1)$ • And the difference is 42 $\\ \implies \sf \: y - x = 12 \: \: ...<klux>EQUATION</klux> \: (<klux>2</klux>)$ $\\ \implies \sf \: y - \frac{5y}{7} = 12 \: \to \: using \: equation(1)$ $\\ \implies \sf \: 7y - 5y = 12 \times 7$ $\implies \sf \: 2y = 84 \:$ $\\ \implies \sf \: \boxed{ \sf\: y = 42} \:$ From equation (2) we get, $\\ \implies \sf \: 42 - x = 12$ $\\ \implies \sf \: 42 - x - 12 = 0$ $\implies \sf \boxed{\sf \: x = 30}$ Hence the larger number is 42 ■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□■□