Question

The average weight of a family is ‘x’ kg. If a guest weighing 40 kg join the family, then the average weight increases by 2 kg. If the weight of this guest had been 28 kg then the average weight of the family including the guest would have decreased by 2 kg. Find ‘x’.
1. 30
2. 32
3. 34
4. 38

Answer 1

Correct Answer - Option 3 : 34

Given:

The average weight of the family = x

The weight of the guest = 40

Then average increases by = 2 kg

Weight of the guest = 28

Average decreases by = 2 kg

Calculations:

Let the number of family members be y.

∴ Total weight = xy

Equation for the first scenario:

⇒ (y + 1) (x + 2) = xy + 40

⇒ xy + x + 2y + 2 = xy + 40

⇒ x + 2y = 38      ----(i)

Equation for the second scenario:

⇒ (y + 1) (x - 2) = xy + 28

⇒ xy + x - 2y - 2 = xy + 28

⇒ x - 2y = 30      ----(ii)

Solving equation (i) and (ii), we get

x = 34.

The value of x is 34.