There are 78 members in group A, 22 members in group B and 34 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are ₹136, ₹383 and ₹457, respectively. The overall average amount (in ₹) spent per member is:

The correct option is 258.

Step 1: Identify the given information

Number of members in Group A, $n_1=78$

Average amount spent per member of Group A, $A_1=₹136$

Number of members in Group B, $n_2=22$

Average amount spent per member of Group B, $A_2=₹383$

Number of members in Group C, $n_3=34$

Average amount spent per member of Group C, $A_3=₹457$

Step 2: Calculate the total amount spent by each group

Total amount spent by Group A = $78\times 136=₹10608$

Total amount spent by Group B = $22\times 383=₹8426$

Total amount spent by Group C = $34\times 457=₹15538$

Step 3: Calculate the total number of members and total amount spent

Total number of members = $78+22+34=134$

Total amount spent = $10608+8426+15538=₹34572$

Step 4: Calculate the overall average amount spent per member

Overall Average = $\frac{\text{Total Amount Spent}}{\text{Total Number of Members}}$

Overall Average = $\frac{34572}{134}=₹258$

Thus, the overall average amount spent per member is ₹258.