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https://web2.0calc.com/questions/ratios-fractions_1

Jul 5, 2021

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2/9 of the pupils in Primary 5 scored an 'A' for a test. The ratio of the number of pupils who scored a 'B' to the number who scored an 'A' was 5 : 3. The rest of the pupils scored a 'C' and a 'D' in the ratio of 6 : 5. The pupils who scored a 'B' were 48 more than the pupils who scored a 'C'.

(a)   How many pupils were there in Primary 5?

(b)   How many pupils failed the test if the failure was a 'D' grade?

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A = 2/9                       A = 6/27

A : B = 3 : 5                                           A + B = 16/27

3/5 = (6/27) / B          B = 10/27

C + D = 11/27            C = 6/27

C : D = 6 : 5

D = 5/27

B / C = 5 / 3

5 / 3 = (48 + C) / C            C = 72

B = 48 + C                         B = 120

C / D = 6 / 5                       D = 60

A = 72

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Total = 324

Ratio:  A : B : C : D = 6 : 10 : 6 : 5

Jul 5, 2021