This is the Multiples Choice Questions Part 2 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.

#### MCQ Topic Outline included in Mathematics Board Exam Syllabi

- MCQ in Age Problems MCQ in Work Problems | MCQ in Mixture Problems | MCQ in Digit Problems | MCQ in Digit Problems |

#### Continue Practice Exam Test Questions Part 2 of the Series

⇐ MCQ in Age, Work, Mixture, Digit, Motion Problems Part 1 | Math Board Exam

**Choose the letter of the best answer in each questions.**

**Problem 51**

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:

A. 49

B. 15

C. 20

D. 18

Answer: **Option B**

Solution:

**Problem 52**

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

A. 15

B. 21

C. 23

D. 27

Answer: **Option C**

Solution:

**Problem 53**

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?

A. 9

B. 4

C. 5

D. 8

Answer: **Option C**

Solution:

**Problem 54**

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?

A. 36 years

B. 24 years

C. 32 years

D. 12 years

Answer: **Option D**

Solution:

**Problem 55**

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?

A. 5

B. 10

C. 15

D. 20

Answer: **Option C**

Solution:

**Problem 56**

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? (ECE November 1995)

A. 16

B. 18

C. 19

D. 20

Answer: **Option B**

Solution:

**Problem 57**

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 children’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?

A. 2

B. 3

C. 4

D. 5

Answer: **Option D**

Solution:

**Problem 58**

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

A. 1500 kg

B. 800 kg

C. 750 kg

D. 500kg

Answer: **Option D**

Solution:

**Problem 59**

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?

A. 40%

B. 30%

C. 45%

D. 35%

Answer: **Option A**

Solution:

**Problem 60**

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?

A. 1:2

B. 3:2

C. 2:3

D. 3:5

Answer: **Option C**

Solution:

**Problem 61**

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?

A. 10

B. 15

C. 20

D. 25

Answer: **Option C**

Solution:

**Problem 62**

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?

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

Answer: **Option B**

Solution:

**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 oz.; Gold = 10.5 oz.

B. Silver = 3.75 oz.; Gold = 11.25 oz.

C. Silver = 5 oz.; Gold = 10 oz.

D. Silver = 7.8 oz.; Gold = 4.2 oz.

Answer: **Option B**

Solution:

**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. ½ hour

B. ½ hour

C. 6 hours

D. 7 hours

Answer: **Option D**

Solution:

**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

C. 10

D. 12

Answer: **Option C**

Solution:

**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

Answer: **Option B**

Solution:

**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 ½ hours. Find how long will it take to fill the pool with the outlet closed.

A. 6

B. 2

C. 3

D. 5

Answer: **Option C**

Solution:

**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. ¾

B. 4/3

C. ½

D. 2/3

Answer: **Option A**

Solution:

**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

Answer: **Option D**

Solution:

**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

Answer: **Option C**

Solution:

**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.

Answer: **Option A**

Solution:

**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

Answer: **Option B**

Solution:

**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.

Answer: **Option B**

Solution:

**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

Answer: **Option D**

Solution:

**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 6th 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

Answer: **Option D**

Solution:

**Problem 76**

On one job, two power shovels excavate 20000 m3 of earth, the larger the shovel working for 40 hours and the smaller shovel for 35 hours. Another job, they removed 40000 m^{3} 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

Answer: **Option A**

Solution:

**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

Answer: **Option A**

Solution:

**Problem 78**

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

A. 9.867 hrs.

B. 9.687 hrs.

C. 8.967 hrs.

D. 8.687 hrs.

Answer: **Option A**

Solution:

**Problem 79**

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

A. 45°

B. 90°

C. 360°

D. 720°

Answer: **Option D**

Solution:

**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

Answer: **Option B**

Solution:

**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

D. 14/11 minutes

Answer: **Option C**

Solution:

**Problem 82**

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

A. 21.41

B. 22.31

C. 21.81

D. 22.61

Answer: **Option C**

Solution:

**Problem 83**

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?

A. 12:33 pm

B. 12:30 pm

C. 12:37 pm

D. 12:287 pm

Answer: **Option A**

Solution:

**Problem 84 (GE February 1997)**

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°?

A. 21.818

B. 12:21.818

C. 21.181

D. 12:21.181

Answer: **Option D**

Solution:

**Problem 85 (GE February 1994)**

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:

A. 360°

B. 120°

C. 540°

D. 720°

Answer: **Option C**

Solution:

**Problem 86**

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?

A. 3:06.06

B. 3:07.36

C. 3:09.36

D. 3:08.36

Answer: **Option A**

Solution:

**Problem 87 (EE October 1990)**

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?

A. 3:27.27

B. 3:31.47

C. 3:22.22

D. 3:44.44

Answer: **Option B**

Solution:

**Problem 88**

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.

A. 5 and 6

B. 7 and 4

C. 1/5 and 1/6

D. 1/7 and ¼

Answer: **Option C**

Solution:

**Problem 89**

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

A. yx

B. 10y + x

C. 10x + y

D. x + y

Answer: **Option B**

Solution:

**Problem 90**

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

A. 70 & 75

B. 60 & 65

C. 65 & 70

D. 75 & 80

Answer: **Option C**

Solution:

**Problem 91**

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.

A. 47

B. 58

C. 63

D. 25

Answer: **Option C**

Solution:

**Problem 92**

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

A. 10 & 12

B. 12 & 14

C. 8 & 10

D. 14 & 16

Answer: **Option A**

Solution:

**Problem 93**

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.

A. 258

B. 567

C. 852

D. 741

Answer: **Option C**

Solution:

**Problem 94**

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

A. 20

B. 21

C. 22

D. 23

Answer: **Option C**

Solution:

**Problem 95**

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

A. 28

B. 50

C. 32

D. 40

Answer: **Option B**

Solution:

**Problem 96**

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

Answer: **Option D**

Solution:

**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

Answer: **Option A**

Solution:

**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

Answer: **Option C**

Solution:

**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

Answer: **Option B**

Solution:

**Problem 100**

Three times the first of the three consecutive odd integers is three more than twice the third. Find the third integer.

A. 9

B. 11

C. 13

D. 15

Answer: **Option D**

Solution:

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

Following is the list of practice exam test questions in this brand new series:

**MCQ in Age, Work, Mixture, Digit, Motion Problems**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

**MCQ from Number 51 – 100**Answer key:

**PART 2**

**MCQ from Number 101 – 150**Answer key:

**PART 3**

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