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Ratios to Percents

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Ratios to Percents:

When parts of a quantity are given to us as ratios, we have seen how to convert them to percentages.

Example

In a class, the ratio of girls to boys is 3: 7.

(i) What percentage of the total number of students is girls and what percentage of the total number of students is boys?

(ii) If the total number of students is 70, what would be the number of girls and what would be the number of boys in the class?

(i) Girls: Boys = 3: 7
Total number of parts = 3 + 7 = 10.

By unitary method:

Girls:
10 → 3(Girls)

1 → `3/10`

100 → `3/10 xx 100` = 30 Girls = 30%

Boys:

10 → 7(Boys)
1 → `7/10`

100 → `7/10 xx 100` = 70 Boys = 70%

(ii) 
In Fraction:

Girls = `3/10 xx 70 = 21`.

Boys = `7/10 xx 70 = 49`.

In Percentage:

Girls = `30/100 xx 70 = 21`.

Boys = `70/100 xx 70 = 49`.

Example

If Rs. 250 is to be divided amongst Ravi, Raju, and Roy so that Ravi gets two parts, Raju three parts, and Roy five parts. How much money will each get? What will it be in percentages?

The parts which the three boys are getting can be written in terms of ratios as 2: 3: 5. Total of the parts is 2 + 3 + 5 = 10.

Amounts received by each Percentages of money for each
`2/10` × Rs. 250 = Rs. 50. Ravi gets `2/10` × 100% = 20%
`3/10` × Rs. 250 = Rs. 75. Raju gets `3/10` × 100% = 30%
`5/10` × Rs. 250 = Rs. 125. Ravi gets `5/10` × 100% = 50%

Example

Last year Giripremi group planted 75 trees. Of these, 48 trees flourished. The Karmavir group planted 50 trees, of which, 35 flourished. Which group was more successful in conserving the trees they had planted?

Suppose the surviving trees of the Giripremi group are A%.
Suppose the surviving trees of the Karmavir group are B%.

The Giripremi’s ratio of the surviving trees to planted trees is `A/100` and also `48/75`.
Therefore, `A/100 = 48/75`.

The Karmavir ratio of the surviving trees to planted trees is `B/100` and also `35/50`.
Therefore, `B/100 = 35/50`.

Let us write the same ratio in two forms,

`"A"/100 = 48/75`

∴ `"A"/100 xx 100 = 48/75 xx 100`

∴ A = 64.

`"B"/100 = 35/50`

∴ `"B"/100 xx 100 = 35/50 xx 100`

∴ B = 70.

∴ The Karmavir group was more successful in conserving the trees they had planted.

Example

In Khatav taluka, it was decided to make 200 ponds in Warudgaon and 300 ponds in Jakhangaon. Of these, 120 ponds in Warudgaon were completed at the end of May, while in Jakhangaon work was complete on 165 ponds. In which village was a greater proportion of the work completed?

Let the number of ponds completed in Warudgaon be A% and in Jakhangaon, B%.

`"A"/100 = 120/120`

`"A"/100 xx 100 = 120/120 xx 100`

A = 60

`"B"/100 = 165/300`

`"B"/100 xx 100 = 165/300 xx 100`

B = 55.

∴ A greater proportion of the work was completed in Warudgaon.

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