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

b) If there was a mark up of 25% on the cost price and a discount of 15% on the sale price, how much would each of the partners have banked at the end of the business day?

Answer 1

Answer: Let's start by setting up some equations based on the given information:

For Tom:

Buys 5 of product A at cost price x

Sells 2 * 5 = 10 of product B at sale price y

Banks Ksh 230,000 at the end of the day

So we have the equation: 5x + 10y = 230,000

For John:

Sells 3 * 5 = 15 of product A at sale price y

Buys 13 of product B at cost price x

Banks Ksh 110,000 at the end of the day

So we have the equation: 15y + 13x = 110,000

Now we can solve for x and y:

From the first equation: x = (230,000 - 10y) / 5 = 46,000 - 2y

Substituting x into the second equation: 15y + 13(46,000 - 2y) = 110,000

Simplifying: 41y = 468,000

So y = 11,400

Substituting y into the first equation: 5x + 10(11,400) = 230,000

Solving for x: x = 35,200

So the price for product A is Ksh 35,200 and the price for product B is Ksh 11,400.

Now, for the second part of the question:

If there was a mark up of 25% on the cost price, the new cost price would be 1.25x for both products A and B.

If there was a discount of 15% on the sale price, the new sale price would be 0.85y for both products A and B.

For Tom:

Buys 5 of product A at new cost price 1.25x = 44,000

Sells 2 * 5 = 10 of product B at new sale price 0.85y = 9690

Banks 10 * 9690 + 5 * (0.85y - 1.25x) = 92,125

For John:

Sells 3 * 5 = 15 of product A at new sale price 0.85y = 9690

Buys 13 of product B at new cost price 1.25x = 44,000

Banks 15 * 9690 - 13 * (1.25x - 0.85y) = 182,065

So Tom would bank Ksh 92,125 and John would bank Ksh 182,065.

Explanation: