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Question
In class X of a school, the ratio of the number of boys to that of the girls is 4 : 3. If there were 20 more boys and 12 less girls, then the ratio would have been 2 : 1, How many students were there in the class?
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Solution
Let the number of students in the class = x
Ratio of boys and girls = 4 : 3
∴ No. of boys = `(4x)/(7)`
and no. of girls = `(3x)/(7)`
According to the problem,
`((4x)/7 + 20) : ((3x)/7 - 12)` = 2 : 1
`(4x + 140)/(7) : (3x - 84)/(7)` : 2 : 1
⇒ `(4x + 140)/(7) xx (7)/(3x - 84) = (2)/(1)`
⇒ `(4x + 140)/(3x - 84) = (2)/(1)`
⇒ 6x – 168 = 4x + 140
⇒ 6x – 4x = 140 + 148
⇒ 2x = 308
⇒ x = `(308)/(2)` = 154
Hence, number of students = 154.
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