Explanation:

Let the number of 20-paise coins be x and the number of 25-paise coins be y. Then,
x + y = 324 (equation 1)
And,
x/5 + y/4 = 71
4x + 5y = 71*20 (Multiplying by 20 on both sides)
Substituting the value of x from equation 1, we get
4(324-y) + 5y = 71*20
1296 – 4y + 5y = 1420
y = 124.