11 Plus Exams Forum

hi, anyone able to help with this question?
65% of juniors wear uniform.
35% seniors wear uniform.
43% of whole school wear uniform
what percentage of whole school are juniors?
thanks!

Where did you get this question?

Sounds like an advanced final question for Independent 11+ schools which is more easily solved using algebra; this shouldn't be in state school 11+ exams

viz. If you let y be the total school population and,
x be the junior population, then (y-x) is the senior population.

Using algebra write down expressions for the information provided.

You then need to re-arrange this expression to give (x/y) x 100 = which is the percentage of junior pupils in the school.

I think the answer works out at 26.67%

I needed algebra too - hence my question.

I tackled it slightly differently but agree on the answer 26.67% [to 2 dp]

Decisiontime639 wrote:hi, anyone able to help with this question?
65% of juniors wear uniform.
35% seniors wear uniform.
43% of whole school wear uniform
what percentage of whole school are juniors?
thanks!

35% of the juniors + 35% of the seniors = 35% of the whole school

so 30% of the junior (65%-35%) is the same as 8% of the whole school

hence number of students in the whole school is 30/8 times the number in the juniors

or the juniors are 8/30=26.67% of the whole school

I used simultaneous equations (j= no of juniors, s = no of seniors, t = total number of pupils)

j + s = t (1)
0.65j + 0.35s = 0.43t (2)

(1) * 0.35 -> 0.35j + 0.35s = 0.35t (3)

(2) - (3) -> 0.3j = 0.08t

j = 0.08/0.3 t
j = 0.267t