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The ratio of the number of boys to that of the girls in a school is 9:7. If the number of girls in the school is 189, then the number of boys in that school will be:
126
243
168
147
243
Since the ratio of boys is 9, the answer must be a multiple of 9. Check the sum of digits: 2+4+3=9, 1+2+6=9, 1+6+8=15, 1+4+7=12. Both 243 and 126 are multiples of 9. Calculate: 189/7=27, then 27├Ч9=243.
Ratio of boys to girls = 9 : 7, Number of girls = 189
B=(79тАЛ)├ЧG
Since the ratio of boys is 9, the answer must be a multiple of 9. Check the sum of digits: 2+4+3=9, 1+2+6=9, 1+6+8=15, 1+4+7=12. Both 243 and 126 are multiples of 9. Calculate: 189/7=27, then 27├Ч9=243.
Confusing the ratio terms and multiplying 189 by 7/9 instead of 9/7, leading to an incorrect result.
Identify Ratio
The ratio of boys (B) to girls (G) is 9:7. This means B/G=9/7.
GBтАЛ=79тАЛ
Set up equation
Given the number of girls G=189, substitute this into the ratio equation.
B=79тАЛ├Ч189
Calculate
Divide 189 by 7 to find the value of one part: 189/7=27. Then multiply by 9 to find the number of boys.
B=9├Ч27=243
B is correct because the ratio 9:7 applied to 189 girls gives 243 boys (189/7=27;27├Ч9=243).
This concept is foundational for mixture and alligation problems where you adjust quantities based on fixed ratios.
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