Algebra 02

20

Ana is 5 years older than Beth. In 5 years, the product of their ages is 1.5 times the product of their present ages. How old is Beth now?

18

Mary is 24 years old. Mary is twice as old as Ana was when Mary was as old as Ana is now. How old is Ana?

7

A father is now 41 and his son 9. After how many years will his age be just triple his son’s age?

5

In a certain family, the sum of the parents’ ages is twice the sum of their children’s ages. Five years ago, the sum of the parents’ ages was four times the sum of the children’s ages during that time. In fifteen years, the sum of the parents’ ages will be equal to the sum of their children’s ages. How many children are there in the family?

84

The age of Diophantus, a Greek mathematician may be calculated from the epitaph which reads as follows: “Diophantus passed 1/6 of his life in childhood, 1/12 in youth, 1/7 as a bachelor. Five years after his marriage was born a son who died 4 years before his father at half his father’s final age.” How old was Diophantus when he died?

20

A 100-kilogram salt solution originally 4% by weight. Salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated?

Pb = 8.8 oz; Ni = 7.2 oz

A pound of alloy of lead and nickel weights 14.4 ounces in water, where lead losses 1/11 of its weight and nickel losses 1/9 of its weight. How much of each metal is in alloy?

19.55%

Ten liters of 25% salt solution and 15%liters of 35% solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration in the mixture?

10

Mr. Brown can wash his car in 15 minutes, while his son John takes twice as long as the same job. If they work together, how many minutes can they do the washing?

2.5 hours

One pipe can fill a tank in 5 hours and another pipe can fill the same tank in 4 hours. A drainpipe can empty the full content of the tank in 20 hours. With all the three pipes open, how long will it take to fill the tank?

10 hrs

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 Peter to paint the same fence if he had to work alone?

8.4

Nonoy can finish a certain job in 10 days if Imelda will help for 6 days. The same work can be done by Imelda in 12 days if Nonoy helps for 6 days. If they work together, how long will it take for them to do the job?

21.81

How many minutes after 10:00 o’clock will the hands of the clock be opposite of the other for the first time?

10 and 12

Find two consecutive even integers such that the square of the larger is 44 greater than the square of the smaller integer.

852

Twice the middle digit of a three-digit number is the sum of the other two. If the number is divided by the sum of its digit, the answer is 56 and the remainder is 12. If the digits are reversed, the number becomes smaller by 594. Find the number.

17.27 km

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 :

68.57 seconds

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 second after they start together in a race around the track in opposite direction?

40

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?

16

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 three items and has taken exactly 1000 on the total sales. How many radios did he sale?

600

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?

8

A number is divided into two parts such that when the greater part is divided by the smaller part, the quotient is 3, and the remainder is 5. Find the smaller number if the sum of the two numbers is 37.

30

Mary was four times as old as Lea ten years ago. If she is now twice as old as Lea, how old is Mary?

27

The sum of three succeeding odd integers is 75. The largest integer is:

4

A ship propelled to move at 25 mi/ hr in still water, travels 4.2 miles upstream in the same time that it can travel 5.8 miles downstream. Find the speed of the stream.

22 hrs

Jose’s rate of doing work three times as fast as Bong. On given day Jose and Bong work together for 4 hours then Bong was called away and Jose finishes the rest of the job in 2 hours. How long would it take Bong to do the complete job alone?

75

The length of a rectangle is 3 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?

5

A particle travels 1 x 106 meters per second in a straight line for 5 x 10-6 seconds. How many meters has it traveled?

8

The area of a trapezoid is 0.5h(b1 + b2), where h is the altitude, and b1 and b2 are the lengths of the parallel bases. If a trapezoid has an alitude of 15 inches, an area of 105 square inches, and one of the bases 22 inches, what is the perimeter, in inches, of the trapezoid?

108.9

If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?

6

A group of 7 friends are having lunch together. Each person eats at least 3/4 of a pizza. What is the smallest number of whole pizzas needed for lunch?

n(100 - r) / 100

There are n students in a school. If r% among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?

255

What is the largest possible product for 2 odd integers whose sum is equal to 32?

5

A solution is made of water and pure acid. If 75% of the solution is water, how many litters of pure acid are in 20 liters of this solution?

40 mins.

Three men A, B, and C can do a piece of work in t hours working together. Working alone, A can do the work in 6 hours more, B in 1 hour more, and C in twice the time if all working together. How long would it take to finish the work if all working together?

2:43.64

What time after 2 o’clock will the hands of the clock extend in opposite directions for the first time?

8 km/hr

A boy on his bicycle to arrive at a certain time to a market that is 30 km from his school. After riding 10 km, he rested for half an hour, and as a result he was obliged to ride the rest of the trip 2 km/hr faster. What was his original speed?

160L

How many liters of a 25% acid solution must be added to 80 liters of a 40% acid solution to have a solution that is 30% acid?

12 MPH

A yacht can travel 10 miles downstream in the same amount of time as it goes 6 miles upstream. If the velocity of the river current is 3MPH, find the speed of the yacht in still water.

2.03 days

A and B working together can finish a job in 5 days, B and c together can finish the same job in 4 days, and A and C in 2.5 days. In how days can all of them do the job working together?

21%

If Chicago is 10% taller than Ishida and Ishida is 10% taller than Chad, then Ichigo is taller than Chad by how many percent?

1%

After the price of petroleum oil went up by 10%, a buyer reduced his oil consumption by the same percent. By what percent would his petroleum bill changed?

100

An organization consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n

5

In a certain family, the sum of the parents’ ages is twice the sum of their children’s ages. Five years ago, the sum of the parents’ ages was four times the sum of the children’s ages during that time. In fifteen years, the sum of the parents’ ages will be equal to the sum of their children’s ages. How many children are there in the family?

420

The excess of the sum of the fourth and fifth parts over the difference of the half and third parts of a number is 119. Find the number.

ywn / (x*c)

If w workers, working at equal rates, can produce x toys in n days, how many days it takes c workers, working at same equal rates, to produce y toys?

7

A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b.

9

If thrice the smaller number exceeds the larger by 12. Find the larger number if the two numbers are consecutive odd integers.

25 kg

Determine how much water should be evaporated from 50kg of 30% salt solution to produce a 60% salt solution. All percentages are by weight.

5.5 mins

A runs around a circular track in 60 seconds, and in 50 seconds. Five seconds after A starts, B starts from the same point in the same direction. When will they be together for the first time, assuming they run around the track continuously?

250

An antelope is now 50 of her leaps ahead of a cheetah which is pursuing her. How many more leaps will the antelope take before it is overtaken if she takes 5 leaps while the cheetah takes 4 leaps, but 2 of the cheetah’s leaps are equivalent to 3 of the antelope’s leaps?

55,000

An investor has P100,000, part of which he invested at 12% interest and the rest at 18%. He received a total annual interest of P15,300. How much did he invest at 18% interest rate?

370

An object travels at fifteen feet per minute. How many feet does it travel in 24 minutes and 40 seconds?

a = 5, b = 6

A number is given as 987562153ab where a and b are digits. Which values of a and b, such that a + b = 11 and a < b, would result in 987562153ab being divisible by 4?

1050

A vendor goes to market to buy fruits for resale at his store. He spends half his money for mangoes, and one-third of what remains for bananas. He spends 150 for other fruits and still has 200 left from the amount he originally had. How much money did he have at the start?

200 and 180

Seven carpenters and 5 masons earn a total of 2,300 per day. At the same rate of pay 3 carpenters and 8 masons earn 2,040. What are the wages per day of the carpenter and a mason?

20 days

A man and a boy can do 15 days a piece of work which would be done by 7 men and 9 boys in 2 days. How long would it take one man do it alone?

34

A certain two-digit numbers is 1 less than five times the sum of its digits. If 9 were added to the number, its digits would be reversed. Find the number.

4 km/hr

A speed boat going across a lake 8 km wide proceeds 2 km at a certain speed and then completes the trip at a speed ½ km/hr faster. By doing this, the speed arrives 10 minutes earlier than if the original speed had been maintained. Find the original speed of the speed boat.

27

An audience of 540 people is seated in rows having the same number of persons in each row. If 3 more persons seat in each row, it would require 2 rows less to seat the audience. How many persons were in each row originally?

4000

A clerk submitted the following reports. The average rate of production of radios is 1.5 units for every 1.5 hrs. work by 1.5 workers. How many radios were produce in one month by 30 men working 200 hrs during the month?

5

A piece of rod of length 52 cm. is cut into two unequal parts. Each part is then bent to form a square. It is found that the total area of the two squares is 97cm2. Find the difference between the sides of each square.

1 hour 12 minutes

It takes pump (A) 4 hours to empty a swimming pool. It takes pump (B) 6 hours to empty the same swimming pool. If the two pumps are started together, at what time will the two pumps have emptied 50% of the water in the swimming pool?

15

Two times the father’s age is 8 more than six times his son’s age. Ten years ago, the sum of their ages was 44. The age of the son is:

23

Peter’s age 13 years ago was 1/3 of his age 7 years hence. How old is Peter?

5

A man is 41 years old and in seven years he will be four times as old as his son is at that time. How old is his son now?

12 years

A father is three times as old as his son. Four years ago, he was four times as old as his son was at that time. How old is his son?

15

The ages of the mother and her daughter are 45 and 5 years, respectively. How many years will the mother be three times as old as her daughter?

18

Mary is 24 years old. Mary is twice as old as Ana was when Mary was as old as Ana is now. How old is Ana?

5

The sum of the parent’s ages is twice the sum of their children’s ages. Five years ago, the sum of the parent’s ages is four times the sum of their fchildren’s ages. In fifteen years the sum of the parent’s ages will be equal to the sum of their children’s ages. How many children were in the family?

500 kg

Two thousand kilogram of steel containing 8% of nickel is to be made by mixing stell containing 14% nickel with another steel containing 6% nickel. How much of the steel containing 14% nickel is needed?

40%

A 40-gram alloy containing 35% gold is to be melted with a 20-gram alloy containing 50% gold. How much percentage of gold is the resulting alloy?

2:3

In what radio must a peanut costing P240.00 per kg. be mixed with a peanut costing P340.00 per kg so that the profit of 20% is made by selling the mixture at 360.00 per kg?

20

A 100-kilogram salt solution originally 4% by weight. Salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated?

Lead = 8.8 ounces; Nickel = 7.2 ounces

A pound of alloy of lead and nickel weights 14.4 ounces in water, where lead losses 1/11 of its weight and nickel losses 1/9 of its weight. How much of each metal is in alloy?

Silver = 3.75 oz.; Gold = 11.25 oz.

An alloy of silver and gold weighs 15 oz. in air and 14 oz. in water. Assuming that silver losses 1/10 of its weight in water and gold losses 1/18 of its weight, how many oz. at each metal are in the alloy?

7 hours

A pump can pump out a tank in 11 hours. Another pump can pump out the same tank in 20 hours. How long it will take both pumps together to pump out the tank?

3

A swimming pool is filled through its inlet pipe and then emptied through its outlet pipe in a total of 8 hours. If water enters through its inlet and simultaneously allowed to leave through its outlet, the pool is filled in 7 ½ hours. Find how long will it take to fill the pool with the outlet closed.

3/4

Three persons can do a piece of work alone in 3 hours, 4 hours and 6 hours respectively. What fraction of the job can they finish in one hour working together?

20 hours

A father and his son can dig a well if the father works 6 hours and his son works 12 hours or they can do it if the father works 9 hours and son works 8 hours. How long will it take for the son to dig the well alone?

12 hours

Peter and Paul can do a certain job in 3 hours. On a given day, they work together for 1 hour then Paul left and Peter finishes the rest work in 8 more hours. How long will it take for Peter to do the job alone?

1.125 hours

A pipe can fill up a tank with the drain open in three hours. If the pipe runs with the drain open for one hour and then the drain is closed it will take 45 more minutes for the pipe to fill the tank. If the drain will be closed right at the start of filling, how long will it take for the pipe to fill the tank?

1.923 hours

Delia can finish a job in 8 hours. Daisy can do it in 5 hours. If Delia worked for 3 hours and then Daisy was asked to help her finish it, how long will Daisy have to work with Delia to finish the job?

20.56

A job could be done by eleven workers in 15 days. Five workers started the job. They were reinforced with four more workers at the beginning of the 6th day. Find the total number of days it took them to finish the job.

173.91

On one job, two power shovels excavate 20000m3 of earth, the larger the shovel working for 40 hours and the smaller shovel for 35 hours. Another job, they removed 40000m3 with the larger shovel working for 70 hours and the smaller working 90 hours. How much earth can the larger shovel move in one hour?

18.9

A and B can do a piece of work in 42 days, B and C in 31 days, and A and C in 20 days. Working together, how many days can all of them finish the work?

9.867 hours

Eight men can dig 150 ft of trench in 7hrs. Three men can backfill 100ft of the trench in 4hrs. The time it will take 10 men to dig and fill 200 ft of trench is:

720°

In two hours, the minute hand of the clock rotates through an angle of:

22

In one day (24 hours), how many times will the hour hand and minute hand of a continuously driven clock be together?

16-4/11 minutes

How many minutes after 3:00 will the minute hand of the clock overtakes the hour hand?

12:33 pm

What time between the hours of 12:00 noon and 1:00 pm would the hour hand and the minute hand of a continuously driven clock be in straight line?

12:21.181

At what time after 12:00 noon will the hour hand and the minute hand of a clock first form a n angle of 120°?

540°

From the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock describes an arc of:

3:06.06

It is now between 3 and 4 o’clock and in twenty minutes the minute hand will be as much as the hour-hand as it is now behind it. What is the time now?

3:31.47

A man left his home at past 3:00 o’clock PM as indicated in his wall clock. Between two to three hours after, he returned home and noticed that the hands of the clock interchanged. At what time did he left his home?

1/5 and 1/6

The sum of the reciprocals of two numbers is 11. Three times the reciprocal of one of the numbers is three more than twice the reciprocal of the other number. Find the numbers.

10y + x

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

65 and 70

One number if five less than the other number. If their sum is 135, what are the numbers?

63

In a two-digit number, the unit’s digit is 3 greater than the ten’s digit. Find the number if it is 4 times as large as the sum of its digits.

22

The product f three consecutive integers is 9240. Find the third integer.

50

The product if two numbers is 1400. If three (3) is subtracted from each number, their product becomes 1175. Find the bigger number.