MCQs in Age, Work, Mixture, Digit, Motion Problems Part III

This is the Multiples Choice Questions Part 3 of the Series in Age, Work, Mixture, Digit, Motion Problems of the Engineering Mathematics topic. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

Multiple Choice Questions Topic Outline

• MCQs in Age Problems MCQs in Work Problems | MCQs in Mixture Problems | MCQs in Digit Problems | MCQs in Digit Problems |

Online Questions and Answers in Age, Work, Mixture, Digit, Motion Problems Series

Following is the list of multiple choice questions in this brand new series:

Age, Work, Mixture, Digit, Motion Problems MCQs

PART 1: MCQs from Number 1 – 50                        Answer key: PART I

PART 2: MCQs from Number 51 – 100                   Answer key: PART II

PART 3: MCQs from Number 101 – 150                   Answer key: PART III

Continue Practice Exam Test Questions Part III of the Series

Choose the letter of the best answer in each questions.

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
• C. 40
• D. 41

Problem 109 (ECE November 1998)

A man rows downstream at the rate of 5mph 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. 2 mi
• 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. 4 kph
• C. 9 kph
• D. 5 kph

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 w when x = 1, y = 4 and z = 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 = 4 and y = 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

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 diameter, and the other is 50 m long and 3 mm in diameter.

• A. R₁ = 0.57 R₂
• B. R₁ = 0.72 R₂
• C. R₁ = 0.84 R₂
• D. R₁ = 0.95 R₂

Problem 117

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?

• A. 1000 lbs.
• B. 1150 lbs.
• C. 1175 lbs.
• D. 1200 lbs.

Problem 118 (ECE November 1995)

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 100lbs through 50 feet, what size of motor is requires to lift 800 lbs. in 40 seconds through a distance of 40 feet?

• A. 48 hp
• B. 50 hp
• C. 56 hp
• D. 58 hp

Problem 119

In a certain department store, the salary of 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 P10000.00, her salary for that month is P900.00. When her sales goes up to P 2000.00 her monthly salary goes up to P1000.00. What must be the value of her sales for the month so that her salary for that month will be P2000.00?

• A. P25000.00
• B. P28000.00
• C. P32000.00
• D. P36000.00

Problem 120

A man sold 100 eggs, eighty of them were sold at gain of 30% while the twenty eggs were sold at a loss of 40%. What is the percentage gain or loss of the whole eggs?

• A. 14%
• B. 15%
• C. 16%
• D. 17%

Problem 121

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

• A. 5%
• B. 15%
• C. 15.15%
• D. 15.76%

Problem 122

Pedro bought two cars, one for P600000.00 and the other for P400000.00. 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. 6% gain
• B. 0% gain
• C. 1.20% gain
• D. 6% loss

Problem 123

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 does the customers actually get?

• A. nothing
• B. 1% discount
• C. 9% discount
• D. they pay 1% more

Problem 124

Kim sold a watch for P3500.00 at a loss of 30% on the cost price. Find the corresponding loss or gain if he sold it for P5050.00.

• A. 1% loss
• B. 10% loss
• C. 1% gain
• D. 10% gain

Problem 125

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.

• A. 7.5%
• B. 5%
• C. 8%
• D. 6.25%

Problem 126

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. 650
• B. 504
• C. 483
• D. 540

Problem 127

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.

• A. 100
• B. 49
• C. 50
• D. 51

Problem 128

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 whole sale price, what is the wholesale price of the slipper?

• A. P18.00
• 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 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 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, 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?

• 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 3⁸⁵⁵.

• A. 3
• B. 9
• C. 7
• D. 1

Problem 139 (ECE April 1998)

Find the 1987^th 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

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
• C. 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 ft²
• B. 15,000 ft²
• C. 20,000 ft²
• D. 22,000 ft²

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^-6 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 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?

• A. 1,275.075 feet
• B. 1,375.575 feet
• C. 1,256.547 feet
• D. 1,249.385 feet

Problem 149 (ME April 1997)

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

• A. 2.3567
• B. 2.4495
• C. 3.2256
• D. 3.8876

Problem 150

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?

• A. 5 km
• B. 10 km
• C. 15 km
• D. 20 km

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