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प्रश्न
The ratio of boys and girls in a class is 5 : 3. If 16% of boys and 8% of girls failed in an examination, then find the percentage of passed students.
उत्तर
Let number of boys be ‘b’ and number of girls be ‘g’
Ratio of boys and girls is given as 5 : 3
b : g = 5 : 3
⇒ `"b"/"g" = 5/3` ...(A)
Failure in boys = 16% = `16/100 xx "b" = (16"b")/100`
Failure in girls = 8% = `8/100 xx "g" = (8"g")/100`
Pass in boys = 100 – 16% = 84% = `84/100 "b"` ...(1)
Pass in girls = 100 – 8% = 92% = `92/100 "g"` ...(2)
From A, we have `"b"/"g" = 5/3`, adding 1 on both sides, we get
`"b"/"g" + 1 = 5/3 + 1`
`("b" + "g")/"g" = (5 + 3)/3 = 8/3`
∴ g = `3/8("b" + "g")` ...(3)
Similarly b = `5/8 ("b" + "g")` ...(4)
Total pass = pass in girls + pass in boys
= (1) + (2)
= `84/100 "b" + 92/100 "g"`
Total pass percentage = `"Total pass"/"Total students" xx 100`
Total pass = boys passed + girls passed
= `((84/100 "b" + 92/100 "g")/("b" + "g")) xx 100`
Substituting (3) and (4) in the above, we get
= `((84/100 "b" + 92/100 "g")/("b" + "g")) xx 100`
= `[(84/100 xx 5/8 ("b" + "g"))/(("b" + "g")) + (92/100 xx 3/8 ("b" + "g"))/(("b" + "g"))] xx 100`
= `84/100 xx 5/8 + 92/100 xx 3/8`
= `[420/800 + 276/800] xx 100`
= `696/800 xx 100`
= 87%
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