Explanation:

- Let's break down the problem:

- A sum of Rs1,180 is to be divided among A, B, and C.

- The shares satisfy the condition: 2 times A’s share = 5 times B’s share = 7 times C’s share.

- Let’s denote:

- 2A = 5B = 7C = k (a constant value).

- From the equations:

- A's share = k/2

- B's share = k/5

- C's share = k/7

- The total sum for A, B, and C:

- (k/2) + (k/5) + (k/7) = 1180

- The least common multiple (LCM) of 2, 5, and 7 is 70:

- Solve for k:

$$

\left(\frac{k}{2} + \frac{k}{5} + \frac{k}{7} \right) \cdot \frac{70}{70} = 1180

$$

- $$

\rightarrow \frac{35k + 14k + 10k}{70} = 1180

$$

- $$

\rightarrow \frac{59k}{70} = 1180

$$

- $$

\rightarrow 59k = 1180 \times 70

$$

- $$

\rightarrow 59k = 82600

$$

- $$

\rightarrow k = \frac{82600}{59} \Rightarrow k = 1400

$$

- Now calculate A's share:

- $$

A = \frac{k}{2} = \frac{1400}{2} = 700

$$

- Options given:

- Rs 500

- Rs 750

- Rs 650

- Rs 700

- ? Rs 700 is the correct option.

.