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Question

There are some red and green apples in a box. If 20 red apples are removed from the box , the number of red apples left will be 1/5 of the total number of apples left. If 20 green apples are removed from the box , the number of red apples will be 1/3 of the total number of apples left.

(a) Find the number of red apples in a box

(b) What fraction of the apples in the box is green

 

Answer

(a)
Scenario 1 : If 20 red apples are removed from the box,
red : green : total
1u : 4u : 5u

red : 1u + 20
green : 4u

Scenario 2 : If 20 green apples are removed from the box,
red : green : total
1p : 2p : 3p
red : 1p

green : 2p + 20
1u + 20 ——- 1p

4u ——- 2p + 20 = 2 x (1u + 20) + 20 = 2u + 60
1u ——- 60/(4 – 2) = 30
30 + 20 = 50

(b)
4u/(5u + 20) = 4 x 30/(5 x 30 + 20) = 12/17

Ans : 50 red apples; (b) 12/17.

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This is a multiple transfer Before After question. 

    After  reverse   Before transfer  after  
Red    1u  +20 1u +20    1u + 20
Green   4u   4u   -20  4u – 20
Total 5u   5u + 20     

(1u + 20) / 1    =(4u – 20)/ 2

2u + 40 = 4u – 20

40 + 20 = 4u – /u

2u = 60

1u = 60 ÷ 2 = 30

a)

30 + 20 = 50

b)

4u = 30 × 4 =120

50 + 120 = 170

120/170 =12/17

 

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