The smallest number of five digits exactly divisible by 476

In how many ways can a committee schedule three speakers for three different meetings if they are all available on any of five possible dates?

A, B and C can complete a piece of work in 10, 12, and 15 days respectively, They started the work together. But A left the work before 5 days of its completion. B also left the work 2 days after A left. In how many days was the work completed?

A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the work.  Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work?

In what proportion must a grocer mix sugar at Rs. 12 a kg and Rs. 7 a   kg Sugar as to make a mixture worth Rs 8. a kg?

Alcohol and water in two vessels A and B are in the ratio 5:3 and 5:4 respectively. In what ratio, the liquid of in both the vessels be mixed to obtain a new mixture in vessel C in the ratio 7:5?

In one glass, milk and water are mixed in the ratio 3:5 and in another glass they are mixed in the ratio 6:1.In what ratio should the content of the two glasses be mixed together so that new mixture contains milk and water in the ratio 1:1?

An alloy contains zinc, copper and tin in the ratio 2:3:1 and an other contains copper, tin and lead in the ratio 5:4:3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in the new alloy will be.