In an Institute if 30% of the numbers of boys were girls, then there would be 50% more numbers of girls than to the number of boys what percentage of the overall class wad girls
Answers
43 per cent of the overall class were girls.
Step-by-step explanation:
Let’s assume the overall class has 100 students, so the number of girls in the class be “x”, then the number of boys in the class will be “100 – x”.
Case 1:
If 30% of the number of boys were girls, so we can write
30 % of [100 - x] = 0.3 * (100 - G) = 30 – 0.3x
∴ The remaining no. of boys = 100 - x - (30 – 0.3x) = 70 – 0.7x ….. (i)
And,
The no. of girls will become = x + 30 – 0.3x = 30 + 0.7x ….. (ii)
Case 2:
Now, the number of girls is 50% more than the number of boys, so we have
No. of boys + [(50/100) * No. of boys] = No. of girls
⇒ No. of boys + [½ * No. of boys] = No. of girls
⇒ 3/2 * [No. of boys] = No. of girls
⇒ 3/2 * [70 – 0.7x] = [30 + 0.7x]
⇒ 3 * [70 – 0.7x] = 2 * [30 + 0.7x]
⇒ 210 – 2.1x = 60 + 1.4x
⇒ 3.5x = 150
⇒ x = 42.85 ≈ 43
Thus,
The percentage of the overall class which were girls, is given by,
= [{No. of girls} / {Total no. of students in the class}] * 100
= [43/100] * 100
= 43%
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