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Example 10: Arrange the following ratios in ascending order.

2 : 5, 3 : 10, 5 : 8, 1 : 3
2 3 5 1
Solution: 2 : 5 = ; 3 : 10 = ; 5 : 8 = ; 1 : 3 =
5 10 8 3
LCM of the denominators 10, 8, 5 and 3 is 120. Then,

2 = 2 × 24 = 48 ; 3 = 3 × 12 = 36
5 5 × 24 120 10 10 × 12 120

5 = 5 × 15 = 75 ; 1 = 1 1 × 40 = 40
8 8 × 15 120 3 3 × 40 120
Q 75 > 48 > 40 > 36

75 48 40 36
\ > > >
120 120 120 120
5 2 1 3
> > >
8 5 3 10

Thus, 5 : 8 > 2 : 5 > 1 : 3 > 3 : 10

Division of a Given Quantity in a Given Ratio

On Dussehra, Shreya’s grandparents gave her `800 to visit the Mela to
celebrate the festival. They asked her to divide the money with her
younger brother Rohan in the ratio 3 : 2.

How will she divide the money with Rohan in the given ratio?
Clearly, there are a total of 5 parts, in which Shreya gets 3 parts of
the amount and Rohan gets 2 parts of the amount.

So, to divide the given quantity in a given ratio, we find the sum of
the terms of the ratio and proceed as follows. Sum of the terms of
given ratio = 3 + 2 = 5
3
Therefore, Shreya’s part of the amount = × `800 = `480
5
2
And Rohan’s part of the amount = × `800 = `320
5
Example 11: Divide `6288 between A, B and C in the ratio 3 : 4 : 5.

Solution: We have, total amount = `6288
Sum of the terms of the ratio = 3 + 4 + 5 = 12
 3  Think and Answer
Therefore, A’s share = `  12 × 6288  = `1572

 4  A chocolate box has 21 chocolate balls
which are to be distributed between you
B’s share = `  12 × 6288  = `2096 and your sibling in the ratio 3:4. What

 5  number of chocolate balls will you and
C’s share = `  12 × 6288  = `2620 your sibling get?


205 Ratio and Proportion