 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that a man bought some oranges at the rate of three dozen oranges for six dollars and the same number of oranges at the rate of six dozen oranges for eight dollars and mixed them. He sold the mixed oranges at the rate of fifteen dozen oranges for thirty dollars. Find the profit or loss percent. First let us find out the least common multiple that is the LCM of three six and fifteen. Let us start with prime number three. Three ones are three. Three twos are six. Three fives are fifteen. Then one, one, five. Then by five, one, one and one. So the LCM will be equal to three into two into five which is equal to thirty. So the LCM of three six and five is equal to three into two into five which is equal to thirty. So now suppose that the man bought thirty oranges of each type. Now for the first type three dozen oranges cost for six dollars. So cost price of three dozen oranges of first type is six dollars which implies cost price of one dozen oranges of first type is equal to six upon three which is equal to two dollars. So cost price of thirty dozen oranges of first type is equal to two into thirty which is equal to sixty dollars. Now for the second type six dozen oranges cost eight dollars. So the cost price of six dozen oranges of second type is eight dollars which implies the cost price of one dozen oranges second type is eight upon six which is equal to four by three dollars. So cost price of thirty dozen oranges of second type is equal to four by three into thirty which is equal to forty dollars. Therefore cost price of sixty dozen mixed oranges is equal to sixty plus forty dollars which is equal to hundred dollars. Now the man sold the mixed oranges at the rate of fifteen dozen oranges for thirty dollars. So the selling price of fifteen dozen mixed oranges is equal to thirty dollars which implies the selling price of one dozen mixed oranges is equal to thirty upon fifteen which is equal to two dollars. So the selling price of sixty dozen mixed oranges is equal to two into sixty which is equal to one twenty dollars. As we know profit is equal to selling price minus cost price this will be equal to one twenty dollars minus hundred dollars which is equal to twenty dollars. So the gain on hundred dollars is equal to twenty dollars which implies gain percent is equal to twenty percent. Hence the man makes a profit of twenty percent which is our answer. This completes our session. Hope you enjoyed this session.