Engineering Mathematics Series of questions, Exams of Engineering Mathematics

Download Engineering Mathematics Series of questions and more Exams Engineering Mathematics in PDF only on Docsity! AGE, WORK, MIXTURE, DIGIT, MOTION PROBLEMS Problem 1: ECE Board April 1995 Kayla is 24 years. Kayla is twice as old as Erin when Kayla was as old as Erin is now. How old is Erin now? A. 16 B. 18 C.12 D.15 Problem 2: EE Board April 1997 The sum of Kim’s and Kevin’s ages is 18. In 3 years, Kim will be as twice as old as Kevin. What are their ages now? A. 4, 14 B.5, 13 C.7,11 D. 6,12 Problem 3: GE Board February 1994 Robert is 15 years older than his brother Stan. However “y” years ago, Robert was twice as old as Stan. If Stan is now “b” years old and b>y, find the value of (b — y). A. 15 B. 16 C.17 D. 18 Problem 4: John is 3 times as old as Jaime. Three years ago, John was four times as old as Jaime. The sum of their ages is? A. 20 B. 24 C. 28 D. 36 Problem 5: A girl, is one-third as old as her brother and 8 years younger than her sister. The sum of their ages is 38 years. How old is the girl? A.4 B.5 C.6 D.7 Problem 6: Maja is now 18 years old and his colleague Angel is 14 years old. How many years ago was Maja twice as old as Angel? A.5 B.7 C.8 D. 10 Problem 7: A father tells his son, | 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.15 B.17 c.19 D. 21 Problem 8: Six years ago, Maya was five times as old Richard. In five years, Maya will be three times as old as Richard. What is the present age of Richard? A.17 B. 16 C.15 D. 14 Problem 9: At present, the sum of the parents’ ages is twice the sum of the children’s ages. Five years ago, the sum of the parent’s ages was 4 times the sum of the children’s ages. Fifteen years hence, the sum of the parents’ ages will be equal to the sum of the children’s ages. How many children are there? A.3 B.4 c.5 D.6 Problem 10: Tom is now twice as old as Jerry. Four years ago, Tom was three times as old as Jerry then. How old is Tom? A.14 B. 16 C. 18 D. 24 Problem 11: ME Board February 1998 A pump can pump out water from a tank in 11 hours. Another pump can pump out water from the same tank in 20 hours. How long will it take both pumps to pump out water in the tank? A. 7 hours B. 6 hours C. 7 1/2 hours D. 6 1/2 hours Problem 12: CE Board November 1993 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? A. 2.00 hours B. 2.50 hours C. 2.25 hours D. 2.75hours Problem 13: A tank is filled with an intake pipe in 2 hours and empties by an outlet pipe in 4 hours. If both pipes are opened, how long will it take to fill the empty tank? A. 3 hours B. 4 hours C. 5 hours D. 6 hours Problem 14: Problem 27: ME Board October 1992 A Chemist of a distillery experimented on two alcohol solutions of different strength, 35% alcohol and 50% alcohol, respectively. How many cubic meters of each strength must he use to produce mixture of 60 cubic meters that contain 40% alcohol? A. 20 m® of solution with 35% alcohol, 40 m° of solution with 50% alcohol B. 50 m° of solution with 35% alcohol, 20 m* of solution with 50% alcohol C. 20 m° of solution with 35% alcohol, 50 m® of solution with 50% alcohol D. 40 m’ of solution with 35% alcohol, 20 m? of solution with 50% alcohol Problem 28: 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? A. 40 B. 35 C. 45 D. 38 Problem 29: ME Board October 1994 Two thousand (2000) kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with another containing 6% nickel. How much of each is needed? A. 1500 kg of steel with 14% nickel, 500 kg of steel with 6% nickel B. 750 kg of steel with 14% nickel, 1250 kg of steel with 6% nickel C. 500 kg of steel with 14% nickel, 1500 kg of steel with 6% nickel D. 1250 kg of steel with 14% nickel, 750 kg of steel with 6% nickel Problem 30: How much water must be evaporated from 10 kg solution which has 4% salt to make a solution of 10% salt? A.4kg B. 5 kg C. 6 kg D. 7 kg Problem 31: EE Board October 1994 If a two digit number has x for its unit’s digit and y for its ten’s digit, represent the number. A.10x+y B. 10y +x C. yx D. xy Problem 32: EE Board October 1994 One number is 5 less that the other. If their sum is 135, what are the numbers? A. 85, 50 B. 80, 55 C. 70, 65 D. 75, 60 Problem 33: ECE Board March 1996 A.6 B.7 Cc. 8 D.9 Problem 34: ECE Board March 1996 The sum of the two numbers is 21 and one number is twice the other. Find the numbers. A. 6,15 B. 7,14 C. 8, 13 D.9, 12 Problem 35: EE Board April 1993 If eight is added to the product of nine and the numerical number, the sum is seventy-one. Find the unknown number. A.5 B.6 C.7 D.8 Problem 36: Find the fraction such that if 2 is subtracted from its term becomes ‘%, but if 4 is added to its terms it becomes ‘2. A. 3/5 B. 5/12 C. 5/14 D. 6/13 Problem 37: GE Board February 1992 The product of 1/4 and 1/5 of a number is 500. What is the number? A. 50 B. 75 C. 100 D. 125 Problem 38: If 3 is subtracted from the numerator of a certain fraction, the value of the fraction becomes 3/5. If 1 is subtracted from the denominator of the same fraction, it becomes 2/3. Find the original fraction. A. 35/55 B. 36/55 C. 3/7 D. 32/41 Problem 39: ECE Board November 1997 The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction. A. 8/5 B. 13/5 C. 5/13 D. 3/5 Problem 40: Find the product of two numbers such that twice the first added to the second equals 19 and three times the first is 21 more than the second. A. 24 B. 32 C. 18 D. 20 Problem 41: The ten’s digit of a number is 3 less than the unit's digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. What is the original number? A. 36 B. 47 C. 58 D. 69 Problem 42: The second of the four numbers is three less than the first the third is four more than the first and the fourth is two more than the third. Find the fourth number if their sum is 35. A. 10 B.11 C.12 D. 13 Problem 43: EE Board April 1997 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. 20 min B. 21 min C. 22 min D. 18 min Problem 44: EE Board April 1997 A boat man rows to a place 4.8 miles with the stream and back in 14 hours, but finds that he can row 14 miles with the stream in the same time as 3 miles against the stream. Find the rate of the stream. A. 1.5 miles per hour B. 1 mile per hour C. 0.8 mile per hour D. 0.6 mile per hour Problem 45: ECE Board November 1998 A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. How far is downstream should he go if he is to return in 7/4 hours after leaving? A. 2.5 miles B. 3.3 miles C. 3.1 miles D. 2.7miles Problem 46: CE Board November 1994 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. 50 B. 60 Cc. 70 D. 40 Problem 47: CE Board May 1998 A boat travels downstream in 2/3 of the time as it goes going upstream. If the velocity of the river's current is 8 kph, determine the velocity of the boat in still water. A. 40 kph B. 50 kph C. 30 kph D. 60 kph Problem 48: Two planes leave Manila for a southern city, a distance of 900 km. Plane A travels at a ground speed of 90 kph faster than the plane B. Plane A arrives in their destination 2 hours and 15 minutes ahead of Plane B. What is the ground speed of Plane A. A. 205 kph A pound of alloy of lead and nickel weighs 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? A. Lead = 7.2 ounces; Nickel = 8.8 ounces B. Lead = 8.8 ounces; Nickel = 7.2 ounces C. Lead = 6.5 ounces; Nickel = 5.4 ounces D. Lead = 7.8 ounces; Nickel = 4.2 ounces Problem 63 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? A. Silver = 4.5 0z.; Gold = 10.5 oz. B. Silver = 3.75 02.; Gold = 11.25 oz. C. Silver = 5 0z.; Gold = 10 oz. D. Silver = 7.8 0z.; Gold = 4.2 oz. Problem 64 (ME April 1998) 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? A. ¥2 hour B. % hour C. 6 hours D. 7 hours Problem 65 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? A.6 B.8 Cc. 10 D. 12 Problem 66 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? A. 2 hours B. 2.5 hours C. 1.92 hours D. 1.8 hours Problem 67 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 “2 hours. Find how long will it take to fill the pool with the outlet closed. op> anh ® D.5 Problem 68 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? A.% B. 4/3 C.% D. 2/3 Problem 69 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? A. 5 hours B. 10 hours C. 15 hours D. 20 hours Problem 70 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? A. 10 hours B. 11 hours C. 12 hours D. 13 hours Problem 71 (ECE November 1995) 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? A. 10 hrs. B. 11hrs. C. 13hrs. D. 15hrs. Problem 72 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? A. 8.9 B. 8.4 C. 9.2 D.8 Problem 73 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? A. 1.15 hrs. B. 1.125 hrs C. 1.325 hrs. D. 1.525 hrs. Problem 74 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? A. 2/5 hours B. 25/14 hours C. 28 hours D. 1.923 hours Problem 75 (CE November 1998) 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 6" day. Find the total number of days it took them to finish the job. A. 22.36 B. 21.42 C. 23.22 D. 20.56 Problem 76 On one job, two power shovels excavate 20000 m° of earth, the larger the shovel working for 40 hours and the smaller shovel for 35 hours. Another job, they removed 40000 m* 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? A. 173.91 B. 347.83 C. 368.12 D. 162.22 Problem 77 (EE April 1996) 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? A. 18.9 B. 19.4 C. 17.8 D. 20.9 Problem 78 Eight men can dig 150 ft of trench in 7 hrs. Three men can backfill 1 00ft of the trench in 4 hrs. The time it will take 10 men to dig and fill 200 ft of trench is: A. 9.867hrs. B. 9.687hrs. C. 8.967hrs. D. 8.687hrs. Problem 79 In two hours, the minute hand of the clock rotates through an angle of : A. 45° B. 90° C. 360° D. 720° Problem 80 In one day (24 hours), how many times will the hour hand and minute hand of a continuously driven clock be together A. 21 B. 22 C. 23 D. 24 Problem 81 How many minutes after 3:00 will the minute hand of the clock overtakes the hour hand? A. 14/12 minutes B. 16-11/12 minutes C. 16-4/11 minutes The sum of the digits of the three-digit number is 14. The hundreds digit being 4 times the units digit. If 594 is subtracted from the number, the order of the digits will be reversed. Find the number. A. 743 B. 563 C. 653 D. 842 Problem 97 (ECE March 1996) The sum of two numbers is 21, and one number is twice the other. Find the numbers. A. 7 and 14 B. 6 and 15 C. 8 and 13 D. 9 and 12 Problem 98 (ECE March 1996) Ten less than four times a certain number is 14. Determine the number. A.4 B.5 C.6 D.7 Problem 99 (ECE November 1997) The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction. A. 8/5 B. 5/13 C. 13/5 D. 3/5 Problem 100 Three times the first of the three consecutive odd integers is three more than twice the third. Find the third integer. AQ B.11 C.13 D.15 Problem 101 Nonoy left Pikit to drive to Davao at 6:15 PM and arrived at 11:45 PM averaged 30 mph and stopped 1 hour for dinner, how far is Davao from Pikit. A. 128 B. 135 C. 160 D. 256 Problem 102 A man fires a target 420 m away hears the bullet strikes to 2 second 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. 525 m/s B. 360 m/s C. 350 m/s D. 336 m/s Problem 103 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 : A. 17.27 km B. 17.72 km C. 12.77 km D. 17.32 km Problem 104 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? A. 58.76 seconds B. 68.57 seconds C. 65.87 seconds D. 86.57 seconds Problem 105 Juan can walk from his home to his office at the rate of 5 mph and back at the rate 2 mph. What is his average speed in mph? A. 2.86 B.3.56 C.4.12 D.5.89 Problem 106 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 a circumference and Kim towards the center, find their distance after 10 minutes. A.193 m B.202 m C.241 m D.258 m Problem 107 Two ferryboats ply back and forth across a river with constant but different speeds, turning at the river banks 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. 1500 m B. 1700 m C. 2000 m D. 2200 m Problem 108 (CE May 1998) 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. 38 B. 39 Cc. 40 D. 41 Problem 109 (ECE November 1998) Aman rows downstream at the rate of 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.2mi B. 3.5 mi C.3 mi D. 2.5 mi Problem 110 (EE April 1997) 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? A. 20 min B. 25 min C. 30 min D. 35 min Problem 111 (CE May 1999) At 2:00 pm, an airplane takes off at 340mph on an aircraft carrier. The aircraft carrier moves due south at 25kph in the same direction as the plane. At 4:05 pm, the communication between the plane and aircraft carrier was lost. Determine the communication range in miles between the plane and the carrier. A. 656 miles B. 785 miles C. 557 miles D. 412 miles Problem 112 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. A. 2 kph B. 4kph C. 9kph D. 5kph Problem 113 (CE May 1993) 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 wwhen x= 1, y=4 andz =2. A.4 B.2 c.1 D.3 Problem 114 (ECE November 1993) If x varies directly as y and inversely as z, and x = 14 when y = 7 and z = 2, find x, when z = 4andy=16. A.14 B.4 C. 16 D.8 Problem 115 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. A. 6000 m B. 7000 m C. 8000 m D. 9000 m Problem 116 B. P17.00 C. P15.00 D. P22.50 Problem 129 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? A. 780 B. 46800 C. 1835 D. 4680 Problem 130 At acertain 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 18000 newspapers? ( Hint: let x = number of machines) A. 50x B. 3000/x C. 50/x D. 3000x Problem 131 (ME April 1996) 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? A. 1 hour B. 0.75 hour C. 3 hours D. 2.25 hours Problem 132 Of the 316 people watching a movie, there a re 78 more children than women and 56 more women than men. The number of men in the movie house is: A. 176 B. 98 C. 42 D. 210 Problem 133 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.Q-(Q/A)t B. Q + (Q/A) t C. Qt-Q/A D. Qt—(Q/A) t Problem 134 (ECE March 1996) A merchant has three items on sale: namely, a radio for P50, a clock for P30, anda 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? A. 80 B.4 C. 16 D. 20 Problem 135 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. 500 B. 550 C. 600 D. 650 Problem 136 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. How many cards are there in the first pile. A.14 B. 15 C. 16 D.17 Problem 137 (ECE November 1997) The population of the Philippines doubled in the last 30 years from 1967 to 1997.Assuming that the rate of population rate increase will remain the same in what year wills the population triple? A. 2030 B. 2027 C. 2021 D. 2025 Problem 138 Determine the unit digit in the expansion of A.3 B.9 C.7 D.1 Problem 139 (ECE April 1998) Find the 1987" digit in the decimal equivalent of 1785/9999 starting from the decimal point. A.1 B.7 c.8 D.5 Problem 140 Find the sum of all positive integral factors of 2048. A. 4095 B. 3065 C. 4560 D. 1254 Problem 141 In how many ways can two integers be selected from the numbers 1,2,3,...50 so that their difference is exactly 5? A. 50 B.5 C. 45 D. 41 Problem 142 855 A box contains 8 balls, 6 black balls.a8 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.8 B.9 Cc. 10 D.11 Problem 143 A shore 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? A. 64 B. 80 C. 72 D. 92 Problem 144 (ME October 1999) An engineer was told that a survey had been made on a certain rectangular field but the dimension had been lost .An assistant remembered that if the field had been 100 ft longer and 25 ft narrower, the area would have been increased by 2500 sq. ft, and that if it had been 100 ft shorter 50 ft wider, the area would have been decreased 5000 sq.ft. What was the area of the field? A. 25.000 ft? B. 15,000 ft? C. 20,000 ft? D. 22,000 ft” Problem 145 (EE April 1994) A 10-meter tape is 5 mm short. What is the correct length in meters? A. 9.995 m B. 10.05 m C. 9.95 m D. 10.005 m Problem 146 (ME OCTOBER 1997) The distance between two points measured with a steel tape was recorded as 916.58 ft. later. The tape was checked and to be only 99.9 ft long. What is the true distance between the points? A. 035.66 ft B. 966.15 ft C. 955.66 ft D. 915.66 ft Problem 147 (ME April 1996) A certain steel tape is known to be 100000 feet long when the temperature of 70°F . When the tape is at a temperature of 10°F, what reading corresponds to a distance of 90 ft? Coefficient of linear expansion of the tape is 5.833 x 10° per °F. A. 85.935 B. 88.031 C. 90.031 D. 93.031 Problem 148 (ME April 1996) 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 tasted when the