Three numbers are in the ratio $$\frac{5}{14} : \frac{16}{13} : \frac{20}{14}$$. The difference between the largest and the smallest number is 30. Find the largest number.

Correct option is A

Given: ​

​$$\frac{5}{14} : \frac{16}{13} : \frac{20}{14}$$ 

Largest number - smallest number = 30 

Solution: ​

​$$\frac{5}{14} : \frac{16}{13} : \frac{20}{14} \\ \ \\ = 65 : 224 : 260$$ 

Now, 

260x - 65x = 30

195x = 30 

x = $$\frac{30}{195} = \frac2{13}$$ 

So, Largest number = $$\frac2{13}\times 260 = 40$$​​