SOLUTION: There are more pupils in School A than School B. 30% of the pupils in School A is 45 more than 40% of the pupils in School B. If 10% of the pupils in School A leaves to join Sc

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: There are more pupils in School A than School B. 30% of the pupils in School A is 45 more than 40% of the pupils in School B. If 10% of the pupils in School A leaves to join Sc      Log On


   

Question 341311: There are more pupils in School A than School B.
30% of the pupils in School A is 45 more than 40% of the pupils in School B.
If 10% of the pupils in School A leaves to join School B, there will be 200 more pupils in School A than School B.
(a) How many pupils are there in School B ?
(b) How many percent less pupils are there in School B than School A ?
Answer by J2R2R(94) About Me  (Show Source):
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Supposing the number of pupils in School A is A and the number of pupils in School B is B.

30% of the pupils in School A is 45 more than 40% of the pupils in School B means

0.3A = 0.4B + 45 … … … (1)

If 10% of the pupils in School A leaves to join School B, there will be 200 more pupils in School A than School B means

0.9A = B + 0.1A + 200 which can be rewritten

0.8A = B + 200 … … … (2)

(1) can be rewritten 3A = 4B + 450. Multiply by 5 gives 15A = 20B + 2250

(2) can be rewritten 8A = 10B + 2000. Multiply by 2 gives 16A = 20B + 4000

Solving gives A = 1750; B = 1200


Checking:

30% of A = 525

40% of B = 480

480 + 45 = 525



0.9 A = 1575

B + 0.1A = 1375

1375 + 200 = 1575



(a) How many pupils are there in School B? 1200 pupils
(b) How many percent less pupils are there in School B than School A? (1750 - 1200)/1750 = 550/1750 = 31.43%