Aman verma wrote:Q: In an organisation, there are total 40 employees belonging to three different departments A , B , and C . Each department has more than 7 employees. The organisation decides to pay a bonus of $ 15,000, $ 10,000 and $ 7,000 to each of the employees of the departments A, B, C respectively . If the total amount paid to the employees as bonus is
$ 429,000 , then the number of employees in department C is :
a)18
b)16
c)15
d)14
e)12
15,000A + 10,000B + 7000C = 429,000
15A + 10B + 7C = 429
15A + 10B = 429 - 7C
The equation above shows us that when 7C is subtracted from 429, the result must be the sum of a multiple of 15 and a multiple of 10.
Now let's examine the answer choices. We need a multiple of 7 that, when subtracted from 429, will yield a value that is the sum of a multiple of 15 and of 10.
Only answer choice E works:
12*7 = 84.
429 - 84 = 345.
The correct answer is
E.
While there is no need to do any more work, here is the complete solution:
Since there are 40 total employees, if C = 12, then A+B = 40-12 = 28.
Thus we get the following 2 equations:
15A + 10B = 345
A+B = 28
Multiplying the second equation by 10, we get:
15A + 10B = 345
10A + 10B = 280
Subtracting the second equation from the first, we get:
5A = 65.
A = 13.
B = 28-13 = 15.
Thus, A=13, B=15, and C=12.
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