Question

Solve the following
In the elections, 1080 of the 1200 women in Jambhulgaon cast their vote, while 1360 of the 1700 in Wadgaon cast theirs. In which village did a greater proportion of women cast their votes?

Answer 1

Total number of women in Jambhulgaon = 1200
Number of women in Jambhulgaon who cast their vote = 1080
Total number of women in Wadgaon = 1700
Number of women in Wadgaon who cast their vote = 1360
Suppose x% women cast their votes in Jambhulgaon and y% women cast their votes in ​Wadgaon.
Let us find the ratio of number of women who cast their vote to the total number of women in each case. We then write those ratios in two forms, obtain equations and solve them. Then, we have
$\frac{x}{100}=\frac{1080}{1200}$ and $\frac{y}{100}=\frac{1360}{1700}$
⇒$\frac{x}{100}\times 100=\frac{1080}{1200}\times 100$ and $\frac{y}{100}\times 100=\frac{1360}{1700}\times 100$
⇒x = 90 and y = 80
∴ 90% women cast their votes in Jambhulgaon and 80% women cast their votes in Wadgaon.
∴ A greater proportion of women cast their votes in Jambhulgaon.