Question

Solve the following.

In the elections, 1080 of the 1200 women in Jambhulgaon cast their vote, while 1360 of 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 the 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

`"x"/100 = 1080/1200` and `"y"/100 = 1360/1700`

⇒ `"x"/100 xx 100 = 1080/1200 xx 100` and

`"y"/100 xx 100 = 1360/1700 xx 100`

⇒ x = 90 and y = 80

∴ 90% of women cast their votes in Jambhulgaon and 80% of women cast their votes in Wadgaon.

∴ A greater proportion of women cast their votes in Jambhulgaon.