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You can read the postings on **Sarin learns concept of ratio in school** and **Sarin learns the concept of Fraction (mathematics concept)** to understand the concept of Ratio and Fraction or Portion.

You should read the posting on **Sarin learns Average Number, Percentage and Charting in school (Math Concept)** to understand about Average Number.

*Challenge yourself with the question before look out for the given solution‼!*

**Upper primary school mathematics question UPQ313**

Hairu had 80 more stickers than Sarin. Hairu gave 25% of his stickers to Sarin. Sarin in return gave 60% of his stickers to Hairu. In the end, Hairu had 100 stickers more than Sarin. How many stickers did Hairu have at first?

Solution:

Start the model base on Hairu had 80 more than Sarin

25% of hairu’s stickers is ¼ fraction of his stickers and we can subdivide the above block by 4

Redraw the model with Sarin received ¼ fraction of Hairu stickers

Sarin gave back 60% of his stickers to Hairu that is given 3/5 fraction of Sarin’s stickers

Hairu finally had 100 stickers more than Sarin

The final model

From the final model

4 units = 100 + 8 – 72 = 36

1 unit = 9

The number of stickers that Hairu had at first = 4 × 9 + 80 = 116

Check:

Sarin had at first = 4 × 9 = 36

25% of Hairu = 116 × 0.25 = 29

Give to Sarin, Sarin had = 36 + 29 = 65

60% of Sarin had = 65 × 0.6 = 39

Hairu finally had = 39 + 116 – 29 = 126

Sarin finally had = 65 – 39 = 26

Hairu had 126 – 26 = 100 more stickers than Sarin finally

Alternative solution(1):

By ratio method

Initial ratio, Hairu had 80 more stickers than Sarin

Hairu : Sarin = (4U + 80) : 4U

Hairu shifted 25% or ¼ fraction of stickers to Sarin

Hairu : Sarin = (3U + 60) : (4U + 1U + 20) = (3U + 60) : (5U + 20)

Sarin gave back 60% or 3/5 fraction of stickers to Hairu

Final ratio

Hairu : Sarin = (3U + 60 + 3U + 12) : (2U + 8) = (6U + 72) : (2U + 8)

The different in stickers finally is 100

6U + 72 – 2U – 8 = 100

4U = 36

1U = 9

The number of stickers Hairu had at first = 4 × 9 + 80 = 116

Alternative solution(2):

By equations,

Set: The number of sticker Hairu had at first = D

The number of stickers Sarin had at first = J

Initially,

D = J + 80

Finally,

75%D + 60% (J + 25%D) = 40% (J + 25%D) + 100

0.75D + 0.2J + 0.05D = 100

8D + 2J = 1000

Solve the equations,

8J + 640 + 2J = 1000

10J = 360

J = 36

The number of stickers Hairu had at first = D = J + 80 = 36 + 80 = 116