If 214 apples were distributed among Ajay, Amit and Amar in the ratio $$\frac{1}{5}:\frac{1}{7}:\frac{1}{6}$$, how many apples did the Amar get?​

Correct option is B

​​Given:

The apples are distributed in the ratio $$\frac{1}{5} : \frac{1}{7} : \frac{1}{6}$$ the shares of Ajay, Amit, and Amar .

The total number of apples is 214.

Solution: 

The least common denominator (LCD) of 5, 7, and 6 is 210.

​So, the ratio becomes:

$$42: 30 : 35$$ 

The total number of parts in the ratio is:

$$42 + 30 + 35 = 107$$ 

Since the total number of apples is 214

Value of each part  $$=\frac{214}{107}= 2$$ 

Amar's share corresponds to 35 parts in the ratio. 

Amar’s apples $$= 35 \times 2 = 70$$ 

Amar gets 70 apples.