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# ratios, fractions

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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 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
+318
+1

Total pupils = x

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
+1622
+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

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jugoslav  Jul 6, 2021
edited by jugoslav  Jul 6, 2021
edited by jugoslav  Jul 6, 2021
#4
+318
0

ThAnks for checking my error you are right

apsiganocj  Jul 16, 2021
#3
+115951
+1
Jul 11, 2021