April 2021

A battalion, 20 miles long, advances 20 miles. During this time, a messenger on a horse travels from the rear of the battalion to the front and immediately turns around, ending up precisely at the rear of the battalion upon the completion of the 20-mile journey. How far has the messenger traveled?

At an ordinary rate a man can row the distance from Pasig to Manila, about 15km, in 5 hours less time than it takes him to return. Could he double his rate, his time to Manila would only be one hour less than his time to Pasig. What is the rate of Pasig River?

In what time would Alberto, Brando and Carlo together do a work if Alberto alone could do it in 6 hours more, Brando alone in 1 hour more, and Carlo alone in twice the time?

Ten stones are placed in a straight line on the ground, at intervals of two feet. ten feet beyond the end of the row is a basket from which a boy starts, picks up the stones, and carries them one at a time to the basket. How far does he run in all?

Three numbers whose sum is 42 are in GP. If 1 is subtracted from the first, 3 from three from the second, and 11 from the third, the remainders will be in AP. Find the smallest number.

The number of revolution per minute of a ball governor required to keep the balls h inches below the point of suspension varies inversely as the square root of h. If the balls are 6 inches below for 40 revolutions per minute, at what speed will they be 1-1/2 inches below?

Albert and Bryan can do a certain task if both work together 3 days and Albert then works alone 1 day. Bryan and Carl can do it if Bryan works 3 days and Carl works 10 days. It would take Carl 9 days longer than it would take Albert to do it alone. How long would Albert take if working alone?

After 4/5 of his mangoes spoiled, Albert bought enough from Bryan so that each then had 1/3 as many as first and Albert had 80 more than Bryan. How many had Albert at first?

Fred is more popular than Pete. Together they have 66 friends but Fred has 6 fewer than the square of the number that Pete has. How many friends does Fred have?