Question

Parcel X is twice as heavy as Parcel Y. The ratio of the mass of Parcel Y to the mass of Parcel Z is 1:3. The total mass of the 3 parcels is 24 kg. What is the mass of Parcel X?

Answer 1

Given:

Mass of parcel X = 2 x Mass of parcel Y

Mass of Parcel Y: Mass of parcel Z = 1:3

The total mass of X, Y, Z = 24Kg

To Find: Mass of parcel X

Solution:

Let the mass of parcel X be 'a'

Let the mass of parcel Y be 'b'

Let the mass of parcel Z be 'c'

Mass of parcel X = 2b           ...(i)

$\frac{Mass of Parcel Y}{Mass of Parcel Z}$ = $\frac{1}{3}$

$\frac{b}{c}$ = $\frac{1}{3}$

On cross multiplication we get

3b = c                                     ....(ii)

Total mass = Mass of X + Mass of Y + Mass of Z

24 = a +  b + c

24 = 2b + b + 3b                   .... From (i) and (ii)

24 = 6b

4 = b

Mass of Parcel X = 2b

                            = 2(4)

                            = 8kg

Therefore, the mass of Parcel X will be 8kg