Three persons X, Y and Z are employed to do a piece of work. X and Y together completed \(\frac{21}{25}\)part of the work. Y and Z together completed \(\frac{8}{25}\)part of the work. If all the 3 agreed to complete the work for ₹3,250, then the amount X receives more than that of Z is 

Given:

X and Y together completed (21/25) part of the work.

Y and Z together completed (8/25) part of the work.

All 3 agreed to complete the work for ₹3,250.

Formula used:

Let the total work = 25 units (as work is assumed to be a whole unit).

Payment is divided among X, Y, and Z in the ratio of their contributions to the work.

Calculation:

Le the work done by X, Y and Z be X , Y and Z respectively.

⇒ So, Work done by X + Y = 21 units  ......(1)

⇒ Work done by Y + Z = 8 units   ...........(2)

⇒ X + Y + Z = 25   .......(3)

Adding eqn (1) and (2)

⇒ X + 2Y + Z = 29   ........(4)

Subtract eqn (3) from eqn (4).

⇒ (X + 2Y + Z) - (X + Y + Z) = 29 - 25

⇒ Y = 4

So, from equation (1) ⇒ X + 4 = 21 ⇒ X = 17

From equation (2) ⇒ 4 + Z = 8 ⇒ Z = 4

⇒ Amount recived by X = 17/25 × ₹3,250 = 2210

⇒ Amount recived by Z = 4/25 × ₹3,250 = 520

⇒ Difference between amount recieved by X and Z = 2210 - 520 = ₹1,690

The correct answer is Option (3).