Assumption/Supposition method


①72 pupils have average mass of 47kg.
Actual total mass = 72 x 47kg = 3384kg


②Assume all pupils are boys.
Total mass would be = 72 x 56 = 4032kg

③Mass that has been overcounted/in excess
= 4032kg - 3384kg
= 648kg

This means the number of boys is too many. We have to replace some of the boys with girls to reduce this excess of 648kg

Average mass of girls = 32kg
Average mass of boys = 56kg

④For every boy we replace with a girl, we take away 56kg from the total and add back 32kg.

Overall decrease in total mass for replacing 1 boy with 1 girl

= 56kg - 32kg
= 24kg


⑤Number of boys to be replaced with girls

= total mass to be reduced ÷ mass reduced for replacement of 1 boy

= 648kg ÷ 24kg

27

This tells you that there are actually only 27 girls.


Check :

Mass of 27 girls = 27 x 32kg = 864kg

Number of boys = 72 - 27 = 45

Mass of boys = 45 x 56kg = 2520kg

Total mass of the pupils

= 2520kg + 864kg
= 3384kg