25 writers, 20 doctors, 18 dentists and 12 bank employees spent altogether ₹ 1,330 in a hotel. However, it was found that 5 writers spent as much as 4 doctors, that 12 doctors spent as much as 9 dentists, and that 6 dentists spent as much as 8 bank employees. Out of the four professional groups, which group spent the maximum amount ?
Bank employees
Dentists
Doctors
Writers
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2018
We are given the following relationships:
1. 5 writers spend as much as 4 doctors: $5w_s = 4d_s \implies w_s = \frac{4}{5}d_s$
2. 12 doctors spend as much as 9 dentists: $12d_s = 9t_s \implies 4d_s = 3t_s \implies t_s = \frac{4}{3}d_s$
3. 6 dentists spend as much as 8 bank employees: $6t_s = 8b_s \implies 3t_s = 4b_s$
Substitute $t_s$ from (2) into (3): $3(\frac{4}{3}d_s) = 4b_s \implies 4d_s = 4b_s \implies d_s = b_s$
So, we have $w_s = \frac{4}{5}d_s$, $t_s = \frac{4}{3}d_s$, and $b_s = d_s$.
The total amount spent is ₹ 1330: $25w_s + 20d_s + 18t_s + 12b_s = 1330$
Substitute the values in terms of $d_s$: $25(\frac{4}{5}d_s) + 20d_s + 18(\frac{4}{3}d_s) + 12d_s = 1330$
$20d_s + 20d_s + 24d_s + 12d_s = 1330$
$76d_s = 1330 \implies d_s = \frac{1330}{76} = 17.5$
Now calculate the amount spent per person for each group:
$d_s = 17.5$
$w_s = \frac{4}{5} \times 17.5 = 14$
$t_s = \frac{4}{3} \times 17.5 = \frac{70}{3} \approx 23.33$
$b_s = 17.5$
Total amount spent by each group:
Writers: $25 \times 14 = 350$
Doctors: $20 \times 17.5 = 350$
Dentists: $18 \times \frac{70}{3} = 6 \times 70 = 420$
Bank Employees: $12 \times 17.5 = 210$
Comparing the total amounts, the Dentists group spent the maximum amount (₹ 420).