Question: A group consisting of 25 teachers 20 engineers, 18 doctors and 12 salesmen visited a fair and spent Rs. 1330 altogether. It was found that 5 teachers spent as much as 4 engineers, 12 engineers spent as much as 9 doctors and 6 doctors spent as much as 8 salesmen. If every person in a professional group spent the same amount, the amount spent by each engineer is
Options:
A) Rs. 18
B) Rs. 17.50
C) Rs. 14
D) Rs. 21
Show Answer
Answer:
Correct Answer: B
Solution:
- Let group of teacher, engineers, doctor and salesman denoted by T, E, D, and S, respectively,
According to the question.
$ 25T+20E+18D+12S=1330 $
Given, $ 5T=4E $
$ \Rightarrow $ $ T=\frac{4}{5}E $
$ \Rightarrow $ $ 12E=9D $
$ \Rightarrow $ $ D=\frac{12}{9}E $
$ \Rightarrow $ $ 6D=8S $
$ S=\frac{6}{8}D=\frac{6}{8}\times \frac{12}{9}E=E $
$ \therefore $ $ 25\times \frac{4}{5}E+20E+18\times \frac{12}{9}E+12E=1330 $
$ \therefore $ $ 76E=1330 $
$ \Rightarrow $ $ E=17.50 $