Question

Tom and John are engaged in buying and selling certain products A and B. Tom BUYS 5 of product A but SELLS twice as much of product B. John on the other hand SELLS three times what Tom BOUGHT of product A and BUYS 13 of product B. At the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh 230,000. Under the assumption that the sale prices for product A and B are the same for the two men, and the costs prices for the products A and B are also the same for the two men, obtain the following: a) The price for product A and the price for product B

Answer 1

Let's assume that the cost price for both products A and B is "C", and the selling price for both products A and B is "S". We can use this information to set up two equations, one for Tom and one for John, that relate the costs and profits for the two products:
Tom: 5C - 2(5S) = P1
John: 3(5C) - 13C = P2
where P1 and P2 are the profits made by Tom and John, respectively.
We know that at the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh
230,000. So we can write:
P1 = 230,000 - 5C
P2 = 110,000 - 18C
Substituting these values into the equations for Tom and John, we get:
5C - 2(5S) = 230.000 - 5C

Simplifying these equations, we get:
10C - 10S = 230,000
2C = 110,000
Solving for C, we get:
C = 55,000
Substituting this value back into the first equation, we can solve for S:
10(55,000) - 10S = 230,000
Simplifying this equation, we get:
S = 32,000

Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.