A man fires a target 420 m away and hears the bullet strike 2 seconds after he pulled the trigger. An observer 525 m away from the target and 455 m from the man heard the bullet strike the target one second after he heard the report of the rifle. Find the velocity of the bullet.

A man travels in a motorized banca at the 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:

It takes Michael 60 seconds to run around a 440-yard track. How long does it take Jordan to run around the track if they meet in 32 seconds after they start together in a race around the track in opposite directions?

Juan can walk from his home to his office at the rate of 5 mph and back at the rate of 2 mph. What is his average speed in mph?

Kim and Ken traveled at the same time at the rate of 20 m/min, from the same point on a circular track of radius 600 m. If Kim walks along the circumference and Ken towards the center, find their distance after 10 minutes.

Two ferryboats ply back and forth across a river with constant but different speeds, turning at the riverbanks without loss of time. They leave the opposite shores at the same instant, meet for the first time 900 meters from one shore, and meet for the second time 500 meters from the opposite shore. What is the width of the river?

A boat takes 2/3 as much time to travel downstream from C to D, as to return. If the rate of the river's current is 8 kph, what is the speed of the boat in still water?

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?

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

At 2:00 pm, an airplane takes off at 340 mph on an aircraft carrier. The aircraft carrier moves due south at 25 kph in the same direction as the plane. At 4:05 pm, the communication between the plane and the aircraft carrier was lost. Determine the communication range in miles between the plane and the carrier.

A boat going across a lake 8 km wide proceed 2 km at a certain speed and then completes the trip at a speed 1/2 kph faster. By doing this, the boat arrives 10 minutes earlier than if the original speed had been maintained. Find the original speed of the boat.

Given that w varies directly as the product of x and y and inversely as the square of z and that w = 4 when x = 2, y = 6, and z = 3. Find w when x = 1, y = 4, and z = 2.

If x varies directly as y and inversely as z, and x = 14 when y = 7 and z = 2, find x when z = 4 and y = 16.

The electrical resistance of a cable varies directly as its length and inversely as the square of its diameter. If a cable 600 meters long and 25 mm in diameter has a resistance of 0.1 ohm, find the length of the cable 75 mm in diameter with resistance of 1/6 ohm.

The electrical resistance offered by an electric wire varies directly as the length and inversely as the square of the diameter of the wire. Compare the electrical resistance offered by two pieces of wire of the same material, one being 100 m long and 5 mm in diameter, and the other is 50 m long and 3 mm in diameter.

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 motors. If it takes 20 seconds for a 5-hp motor to lift 50 lbs. through 40 feet, what weight can an 80-hp motor lift through a distance of 40 feet within 30 seconds?

The time required by an elevator to lift a weight, vary 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 motor is required to lift 800 lbs. In 40 seconds through a distance of 40 feet?

In a certain department store, the monthly salary of a saleslady is partly constant and varies as the value of her sales for the month. When the value of her sales for the month is P10,000.00, her salary for that month is P900.00. When her sales go up to P12,000.00, her monthly salary goes up to P1,000.00. What must be the value of her sales for the month so that her salary for that month will be P2,000.00?

A man sold 100 eggs. Eighty of them were sold at a profit of 30% while the rest were sold at a loss of 40%. What is the overall percentage profit or loss?

The population of the country increases 5% each year. Find the percentage it will increase in three years.

Pedro bought two cars, one for P600,000.00 and the other for P400,000.00. He sold the first at a gain of 10% and the second at a loss of 12%. What was his total percentage gain or loss?

A grocery owner raises the prices of his goods by 10%. Then he starts his Christmas sale by offering the customers a 10% discount. How many percent of discount do the customers actually get?

Kim sold a watch for P3,500.00 at a loss of 30% on the cost price. Find the corresponding loss or gain if he sold it for P5,050.00.

By selling balut at P5.00 each, a vendor gains 20%. The cost price of egg rises by 12.5%. If he sells the balut at the same price as before, find his new gain in percent.

The enrollment at college A and college B both grew up by 8% from 1980 to 1985. If the enrollment in college A grew up by 800 and the enrollment in college B grew up by 840, The enrollment at college B was how much greater than the enrollment in college A in 1985?

A group consists of n boys and n girls. If two of the boys are replaced by two other girls, then 49% of the group members will be boys. Find the value of n.

On his Christmas Sale, a merchant marked a pair of slipper P180.00, which is 20% off the normal retail price. If the retail price is 50% higher than the wholesale price, What is the wholesale price of the slipper?

A certain Xerox copier produces 13 copies every 10 seconds. If the machine operates without interruption, how many copies will it produce in an hour?

At a certain printing plant, each of the machines prints 6 newspapers every second. If all machines work together but independently without interruption, How many minutes will it take to print the entire run of 18,000 newspapers?

A manufacturing firm maintains one product assembly line to produce signal generators. Weekly demand for the generators is 35 units. The line operates for 7 hours per day, 5 days per week. What is the maximum production time per unit in hours required for the line to meet the demand?

Of the 316 people watching a movie, there are 78 more children than women and 56 more women than men. The number of men in the movie house is:

A certain department store has an inventory of Q units of a certain product at time t = 0. The store sells the product at a steady rate of Q/A units per week, and exhausts the inventory in A weeks. The amount of product in inventory at any time t is:

A merchant has three items on sale: namely, a radio for P50, a clock for P30, and a flashlight for P1. At the end of the day, she has sold a total of 100 of the three items and has taken exactly P1000 on the total sales. How many radios did he sell?

The price of 8 calculators ranges from P200 to P1000. If their average price is P950, what is the lowest possible price of any one of the calculators?

A deck of 52 playing cards is cut into two piles. The first pile contains 7 times as many black cards as red cards. The second pile contains the number of red cards that is an exact multiple as the number of black cards that is. How many cards are there in the first pile?

The Population of the Philippines doubled in the last 30 years from 1967 to 1997. Assuming that the rate of population increase will remain the same in what year will the population triple?

Determine the unit’s digit in the expansion of $$3^{8555}$$ .

Find the 1987th digit in the decimal equivalent of 1785/9999 starting from the decimal point.

Find the sum of all positive integral factors of 2048.

In how many ways can two integers be selected from the numbers 1,2,3,...50 so that their difference is exactly 5?

A box contains 8 white balls, 15 green balls, 6 black balls, 8 red balls, and 13 yellow balls. How many balls must be drawn to ensure that there will be three balls of the same color?

A shoe store sells 10 different sizes of shoes, each in both high-cut and low-cut variety, each either rubber or leather, and each with white or black color. How many different kinds of shoes does he sell?

An engineer was told that a survey had been made on a certain rectangular field but that the dimensions had been lost. An assistant remembered that if the field had been 10 ft longer and 25 ft narrower, the area would have been increased by 2500 sq. ft, and that if it had been 10 ft shorter and 50 ft wider, the area would have been decreased 5000 sq. ft. What was the area of the field?

A 10-meter tape is 5 mm short. What is the correct length in meters.

The distance between two points measured with a steel tape was recorded as 916.58 ft. Later, the tape was checked and found to be only 99.9 ft long. What is the true distance between the points?

A certain steel tape is known to be 100,000 feet long at a temperature of 70 °F. When the tape is at a temperature of 10 °F, what tape reading corresponds to a distance of $$90 ft$$ ? Coefficient of linear expansion of the tape is $$5.833 \times 10^{-6}$$ per °F.

A line was measured with a steel tape when the temperature was 30 °C. The measured length of the line was found to be 1,256.271 feet. The tape was afterwards tested when the temperature was 10 °C and it was found to be 100.042 feet long. What was the true length of the line if the coefficient of expansion of the tape was 0.000011 per °C?

The standard deviation of the numbers 1, 4, & 7 is:

Three cities are connected by roads forming a triangle, all of different lengths. It is 30 km around the circuit. One of the roads is 10 km long and the longest is 10 km longer than the shortest. What is the length of the longest road?

How many terms of the sequence -9, -6, -3, ... must be taken so that the sum is 66?

The sum of the progression 5, 8, 11, 14 ... is 1025. How many terms are there?

There are seven arithmetic means between 3 and 35. Find the sum of all the terms.

There are nine (9) arithmetic means between 11 and 51. The sum of the progression is;

The sum of all even numbers from 0 to 420 is:

Which of the following numbers should be changed to make all the numbers form an arithmetic progression when properly arranged?

The first term of an arithmetic progression (A.P.) is 6 and the 10th term is 3 times the second term. What is the common difference?

The sum of five arithmetic means between 34 and 42 is:

The positive value of a so that 4x, 5x + 4, 3x2 - 1 will be in arithmetic progression is:

Solve for x if x + 3x + 5x + 7x + ... + 49x = 625.

The 10th term of the series a, a – b, a – 2b, ... is:

If the sum of the first 13 terms of two arithmetic progressions are in the ratio 7:3, find the ratio of their corresponding 7th term.

If 1/x, 1/y, 1/z are in arithmetic progression, then y is equal to:

Find the 30th term of the A.P. 4, 7, 10 ...

Find the 100th term of the sequence 1.01, 1.00, 0.99...

The sum of all numbers between 0 and 10,000 which is exactly divisible by 77 is:

What is the sum of the following finite sequence of terms? 18, 25, 32, 39, ..., 67.

Find x in the series: 1, 1/3, 0.2, x.

Find the fourth term of the progression 1/2, 0.2, 0.125, ...

The 10th term of the progression 6/5, 4/3, 3/2, ... is:

The geometric mean of 4 and 64 is:

What is the formula for the average of two numbers a and b?

Determine the sum of the infinite geometric series of 1, – 1/5, +1/25, ...?

There are 6 geometric means between 4 and 8748. Find the sum of all the terms.

Find the sum of the infinite geometric progression 6, –2, 2/3...

Find the sum of the first 10 terms of the Geometric Progression 2, 4, 8, 16, ....

The 1st, 4th, and 8th terms of an A.P. are themselves geometric progression (G.P.). What is the common ratio of the G.P.?

Determine x so that x, 2x + 7, 10x – 7 will form a geometric progression.

The fourth term of a geometric progression is 189 and the sixth term is 1701, the 8th term is:

The sum of three numbers in arithmetical progression is 45. If 2 is added to the first number, 3 to the second, and 7 to the third, the new numbers will be in geometrical progression. Find the common difference in A.P..

The geometric mean and the harmonic mean of two numbers are 12 and 36/5 respectively. What are the numbers?

If x, 4x + 8, 30x + 24 are in geometric progression, find the common ratio.

A besiege fortress is held by 5700 men who have provisions for 66 days. If the garrison loses 20 men each day, for how many days can the provision hold out?

If one third of the air in the tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes?

A rubber ball is dropped from a height of 15 m. On each rebound, it rises 2/3 of the height from which it last fell. Find the distance traveled by the ball before it comes to rest.

In the recent Bosnia conflict, the NATO forces captured 6400 soldiers. The provisions on hand will last for 216 meals while feeding 3 meals a day. The provisions lasted 9 more days because of daily deaths. At an average, how many died per day?

To build a dam, 60 men must work 72 days. If all 60 men are employed at the start but the number is decreased by 5 men at the end of each 12-day period, how long will it take to complete the dam?

In a benefit show, a number of wealthy men agreed that

the first one to arrive would pay 10 centavos to enter and each later

arrival would pay twice as much as the preceding man. The total

amount collected from all of them was P104,857.50. How many wealthy

men had paid?

Evaluate the following determinant:

The following equation involves two determinants:

The value of x is:

Evaluate the following determinant:

Compute the value of x from the following:

Evaluate the following determinant:

In a class of 40 students, 27 students like Calculus and 25 like

Geometry. How many students liked both Calculus and Geometry?

A class of 40 took examination in Algebra and Trigonometry: If 30

passed Algebra, 36 passed Trigonometry, and 2 failed in both

subjects, the number of students who passed the two subjects is:

The probability for the ECE board examinees from a certain school to

pass the Mathematics subject is 3/7 and that for the Communications

subject is 5/7. If none of the examinees failed in both subjects and there are 4 examinees who pass both subjects, how many examinees from the school took the examination?

In a commercial survey involving 1000 persons on brand preferences, 120 were found to prefer brand x only, 200 persons prefer brand y only, 150 persons prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x, and 370 prefer either brand z or x but not y, and none prefer all the three brands at a time. How many persons have no brand preference with any of the three brands?