Of the 20 girls in a class 16 play hockey, 12 play tennis and 4 play basketball. Every girl plays atleast one game and two plays all the three games. How many girls play two and only two games.
Let's use the principle of inclusion-exclusion to solve this problem.
First, let's add up the number of girls playing each game:
16 + 12 + 4 = 32
However, this counts the girls who play multiple games more than once. Let's subtract them:
32 - 2x = 20
(where x is the number of girls who play all three games)
Simplifying this equation gives:
2x = 12
x = 6
Therefore, there are 6 girls who play all three games. Now we can add up the number of girls playing two or three games:
6 + y = z
(where y is the number of girls playing two games only and z is the total number of girls playing two or three games)
We know that there are 20 girls in total, so:
y + z = 20
Substituting in the equation for z gives:
y + 6 + y = 20
2y = 14
y = 7
So there are 7 girls who play two games only.
The following are the XYZ Co. Ltd figures compile accounts receivable ledger accounts payable ledger control accounts for the month, and ascertain what the net balances of respective ledgers should be on 31 January 2018.
Balance as at 1 January 2018
Accounts receivable ledger Dr. 46462
Cr. 245
Accounts payable ledger Dr. 1472
Cr. 25465
Totals for the month of 31 January 2018
Purchases 76474
Sales 126024
Purchase returns. 2154
Debtors settled by contra accounts with creditors. 455
Bad debts written off 1253
Discounts and allowance to customers 746
Cash received from customers. 120464
Cash discount received. 1942
Cash Paid to creditors 70476
Cash Paid to customers 52