A Chemist of a distillery experimented on two alcohol solutions of different strengths, 35% alcohol and 50% alcohol respectively. How many cubic meters of each strength must he use on order to produce a mixture of 60 cubic meters that contain 40% alcohol?

How much water must be evaporated from a 10 kg solution which has 4% salt to make a solution of 10% salt?

If a two-digit number has x for its unit's digit and y for its ten's digit, represent the number.

Ten less than four times a certain number is 14. Determine the number.

Find the fraction such that if 2 is subtracted from its terms becomes 1/4, but if 4 is added to its terms it becomes 1/2.

A jogger starts a course at a steady rate of 8 kph. Five minutes later, a second jogger starts the same course at 10 kph. How long will it take the second jogger to catch the first?

A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. How far downstream should he go if he is to return in 7/4 hours after leaving?

An airplane flying with the wind took 2 hours to travel 1000 km and 2.5 hours in flying back. What was the wind velocity in kph?

A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at 3/5 of its former rate and arrives three hours after time; but had the accident happened 50 miles farther on the line, it would have arrived one and one-half hour sooner. Find the length of the journey.

In how many minutes after 2 o'clock will the hands of the clock extend in opposite directions for the first time?

What time after 3 o'clock will the hands of the clock be together for the first time?

A man left his home at past 3:00 o'clock PM as indicated in his wall clock, between 2 to 3 hours after, he returns home and noticed the hand of the clock interchanged. At what time did the man leave his home?

A storage battery discharges at a rate that is proportional to the charge. If the charge is reduced by 50% of its original value at the end of 2 days, how long will it take to reduce the charge to 25% of its original charge?

The electric power which a transmission line can transmit is proportional to the product of its design voltage and current capacity, and inversely to the transmission distance. A 115-kilovolt line rated at 100 amperes can transmit 150 megawatts over 150 km. How much power, in megawatts can a 230 kilovolts line rated at 150 amperes transmit over 100 km?

The time required for an elevator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motor. If it takes 30 seconds for a 10 hp motor to lift 100 lbs through 50 feet, what size of the motor is required to lift 800 lbs in 40 seconds through 40 feet.

A group of EE examinees decided to hire a mathematics tutor from Excel Review Center and planned to contribute an equal amount for the tutor's fee. If there were 10 examined, each would have paid P2.00 less. However, if there were 5 less examinees, each would have paid P2.00 more. How many examinees are there in the group?

In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate and of the females 70% are literate. What is the female population?

A merchant has three items on sale, namely a radio for P50.00, a clock for P30.00, and a flashlight for P1.00. At the end of the day, he sold a total of 100 of the three items and has taken exactly P1,000 on the total sales. How many radios did he sell?

The arithmetic mean of a and b is:

If the first term of an arithmetic progression is 25 and the fourth term is 13, what is the third term?

How many terms of the progression 3, 5, 7, ... must be taken in order that their sum will be 2600?

Find the sum of 4 geometric means between 160 and 5.

The fourth term of a G.P. is 216 and the 6th term is 1994. Find the 8th term.

Determine x so that: x, 2x + 7, 10x - 7 will be a geometric progression.

A man mailed 10 chain letters to ten of his friends with a request to continue by sending a similar letter to each of their ten friends. If this continues for 6 sets of letters and if all responded, how much will the Philippines Postal Office earns if the minimum postage costs P 4.00 per letter?

Determine the sum of the infinite series:

A club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many likes both?

The probability for the ECE board examinees from a certain school to pass the subject Mathematics is 3/7 and the subject Communications is 5/7. If none of the examinees fails both subjects and there are 4 examinees who pass both subjects, find the number of examinees from that school who took the examinations.

How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the word "personnel"?

Five different mathematics books, 4 different electronics books, and 2 different communications books are to be placed on a shelf with the books of the same subject together. Find the number of ways in which the books can be placed.

What is the number of permutations of the letters in the word BANANA?

Four different colored flags can be hung in a row to make the coded signal. How many signals can be made if a signal consists of the display of one or more flags?

There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns 5 tickets?

In a throw of two dice, the probability of obtaining a total of 10 or 12 is?

A coin is tossed 3 times. What is the probability of getting 3 tails up?

From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that both balls are white. Assume that the first ball is returned before the second ball is drawn.

Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards.

The angle subtended by an arc is  $24\degree$ . If the radius of the circle is 45 cm, find the length of arc.

A certain angle has a supplement 5 times its complement. What is the angle?

Find the sum of the interior angles of the vertices of a five-pointed star inscribed in a circle.

In triangle ABC, angle C = $70\degree$ , A =  $45\degree$ , AB = 40. What is the length of the median drawn from a vertex A to side BC?  

A circle with a radius of 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border.

The area of a triangle inscribed in a circle is 39.19 sq. cm. and the radius of the circumscribed circle is 7.14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side.

The area of a triangle is 8346 sq. m. and two of its interior angles are $37\degree25'$ and  $56\degree17'$ . What is the length of the longest side?