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avatar+70 

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 pupils scored a 'C' and a 'D' in the ratio 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?

 Jul 2, 2021
 #1
avatar+177 
+2

Total pupils = x 

2x/9 scored A grade. 

No. Of pupils who scored B = y 

Now y/ 2x/9 = 5/3

      9y/2x=5/3 

      y/x   =  10/27 - eq (1) 

Now assume 

   No of pupils who scored C = A

   No of pupils who scored D = B

Now 

   A/B  = 6/5 - eq(2) 

Now given

  y = A+48 -eq (3) 

Now we can write 

2x/9 + A+ B + Y = x

A+ B + Y = 7x/9

Put value of eq (3) 

B+ y-48+y= 7x/9

2y+B-48= 7x /9

Now put value of eq (2) 

5A/6 +2y -48 = 7x/9

(Put A = y-48) 

5(y-48) /6 +2y -48 = 7x/9

5y/6  - 40 +2y -48 = 7x/9

17y/6 -88 = 7x/9

Put value of eq(1)

17(10x/27) /6  -88 = 7x/9

170x/162  -7x/9  = 88  

  (170x - 126x)/162 = 88

  44x/ 162 = 88

    x = 162 * 2

   x = 324 

a)  total pupils (x) = 324

b) no. Of pupils of scores D grade = 

First of all  y/x = 10/27

                    y = 10*324/27  = 120

Now A = y- 48 = 120-48 = 72 

Now

 A/ B = 6/5

B = 72 *5/6

B = 45

So no of pupils who failed = 45

 Jul 2, 2021
 #2
avatar+1425 
+3

Hello, apsi! All that in red ink is wrong!

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Now                                                                                              A = 72

 A/ B = 6/5                                                                                    B = 120

B = 72 *5/6                                          Thi is incorrect!!!            C = 72

B = 45                                                                                           D = 60

So no of pupils who failed = 45                                              Total = 324 laugh

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jugoslav  Jul 6, 2021
edited by jugoslav  Jul 6, 2021
edited by jugoslav  Jul 6, 2021
 #4
avatar+177 
0

ThAnks for checking my error you are right

apsiganocj  Jul 16, 2021
 #3
avatar+114044 
+1
 Jul 11, 2021

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