A sum of Rs. 3170 is divided among X, Y and Z such that if Rs. 13, Rs. 12 and Rs. 18 will be diminished from the shares of X, Y and Z respe…

Let the initial shares of X, Y, Z be x, y, z respectively

Given the total amount with them together is Rs. 3170

Therefore x + y + z = 3170 ----(1)

Given that after diminishing the share by certain amount, the remaining amount with X, Y, Z will be in the ratio 20 : 18 : 21

Let us consider the amount with each of them is X = 20k, Y = 18k, Z = 21k

The actual share left over with each of them after diminishing is x - 13, y - 12 and z - 18 with X, Y, Z respectively

Substituting the new values in Equation 1 we get,

⇒ (x - 13) + (y - 12) + (z - 18) = 20k + 18k + 21k

⇒ (x + y + z) - (13 + 12 + 18) = 59k

⇒ 3170 - 43 = 59k

⇒ k = 3127/59 = 53

Initial share with Z = 21k + 18 = (21 × 53) + 18 = 1113 + 18 = 1131

∴ Initial share with Z = Rs. 1131