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

To solve such questions, make equations as under and then use the options to solve

15x + 10 y + 7 z =429 where x, y, z are the number of people in each of the departments

x +y +z =40

Now put values from the options.. e.g. if z =18 then

15x + 10 y + 7 * 18 = 429 or 15 x +10 y = 429 -126

15x +10y = 313 ... but for x, and y as natural numbers we can never satisfy this equation .. thus 18 cant be the number of members in dept C

Now plug in the last option z =12

15x +10y +7 *12 =429

15x +10 y = 345 .....(.1)

also we get x + y =28 ...... (2)


on solving eq 1 and Eq2 we get x=13 and y =15


therefore from the given option only option E satisfies our conditions and hence should be the answer

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

15a + 10b +7c = 429
a = 40 -b -c

=> 15(40-b-c)+10b+7c=429
=> 5b + 8c = 171
=> b = (171-8c)/5

since b is an integer, (171-8c) should be divisible by 5.
(171-8c) can be divisible by 5 if and only if 8c has a units digit of 1 or 6.
8c cannot have a units digit of 1, so the units digit must be 6.
If 8 multiplied by a number is to result in something that has a unit's digit of 6, the unit's digit of that number must be 2.
The answer must be E -> since 12*8 = 96
c= 12
b = 15
a= 13

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.

OAE