₹10,415 is divided among P, Q, and R in such a way that if ₹62, ₹17, and ₹79 are deducted from their respective shares, they have money in the ratio 15:10:14.

et the original shares of P, Q  and R be P, Q, R  respectively.

After deductions:

• P’s share = P - 62

• Q’s share = Q - 17

• R’s share = R - 19

These are in the ratio 15:10:14:

$P - 62 : Q - 17 : R - 79 = 15 : 10 : 14$

Let the common multiple be $x$:

$P - 62 = 15x \implies P = 15x + 62$
$Q - 17 = 10x \implies Q = 10x + 17$
$R - 79 = 14x \implies R = 14x + 79$

Total sum: $P + Q + R = 10415$

Substitute:

$(15x + 62) + (10x + 17) + (14x + 79) = 10415$

$39x + 158 = 10415$

$39x = 10415 - 158 = 10257$

$x = \frac{10257}{39} = 263$

Now calculate Q and R:

$Q = 10x + 17 = 10 \cdot 263 + 17 = 2647$
$R = 14x + 79 = 14 \cdot 263 + 79 = 3761$

Difference between Q and R:

$R - Q = 3761 - 2647 = 1114$