A father tells his son, I was your age now when you were born”. If the father is now 38 years old, how old was his son 2 years ago?

A 400-mm pipe can fill the tank alone in 5 hours and another 600-mm pipe can fill the tank alone in 4 hours. A drain pipe 300-mm can empty the tank in 20 hours. With all the three pipes open, how long will it take to fill the tank?

Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar, and together they can paint a given fence in 4 hours. How long will it take Pedro can paint the same fence if he had to work alone?

A man travels in a motorized banca at rate of 12 kph from his barrio to the poblacion and come back to his barrio at the rate of 10 kph. If his total time of travel back and forth is 3 hours and 10 minutes, the distance from the barrio to the poblacion is :

Find the value of k so that 4x² + 6x + k is a perfect square.

The expression x⁴ + ax³ + 5x² + bx + 6 when divided by (x – 2) leaves a remainder of 16 and when divided by (x + 1) leaves a remainder of 10. Find a and b.

Find the middle term in the expansion (2x – 1y²)⁶

On one job, two power shovels excavate 20,000 cubic meters of earth, the larger shovel working 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each remove in 1 hour working alone?

A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold?

From the top of a lighthouse 212 ft above a lake, the keeper spots a boat sailing directly towards him. He observes the angle of depression of the boat to be 6º 13’ and then later to be 13º 7’. Find the distance the boat has sailed between the observations.

A tower 150 m high is situated at the top of a hill. At a point 650 m down the hill the angle between the surface of the hill and the line of sight to the top of the tower is 12°30’. Find the inclination of the hill to the horizontal plane.

Find the area of a triangle with sides 23 cm, 26 cm and 31 cm to the nearest ten square centimeters.

When the angle of elevation of the sun is 64°, a telegraph pole that is tilted at an angle of 9° directly away from the sun casts a shadow 21 feet long on the level ground. Find the length of the pole in feet.

If sin A = 3/5, and A is in quadrant II, while cos B = 7/25, and B is in quadrant I. Find sin (A + B).