There are 40 coins in a bag. They are of ₹5 and ₹10 denominations and the total amount of money added together is ₹310. What is the difference between the amount of money in all ₹10 coins and the amount of money in all ₹5 coins?

Total number of coins = 40
Denominations of coins = ₹5 and ₹10
Total amount of money = ₹310

Let:
x = number of ₹5 coins
y = number of ₹10 coins

The total number of coins:

x + y = 40

x = 40 − y  .....(1)

The total value of the coins:
5x + 10y = 310  ...(2)

Equation (1) put in equation (2),

5(40−y) + 10y = 310
200 − 5y + 10y = 310
200 + 5y = 310
5y = 110
y = 22

Put y = 22 into equation 1;

x + 22 = 40
x = 18

The total amount of money in ₹10 coins = 10 × 22 = 220

The total amount of money in ₹5 coins = 5 × 18 = 90

The difference between the amount of money in ₹10 coins and ₹5 coins = 220 − 90 = 130

So, The difference is ₹130.

Thus, the correct answer is (b).