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# MCQ in Algebra and General Mathematics Part 4 | ECE Board Exam

This is the Multiple Choice Questions Part 4 of the Series in Algebra and General Mathematics topics in Engineering Mathematics. 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 Algebraic functions | MCQ in theory of Equations | MCQ in Factorization and Algebraic functions | MCQ in Ratio, Proportion and Variation | MCQ in Matrix theory | MCQ in Arithmetic and Geometric Progression | MCQ in Equations and Inequalities | MCQ in Linear and Quadratic Equations | MCQ in Complex Number System | MCQ in Polynomials | MCQ in Mathematical Induction | MCQ in Logic and Probability | MCQ in Statistics| MCQ in System of Numbers and Conversion | MCQ in Fundamentals in Algebra | MCQ in Binomial Theorems and Logarithms | MCQ in Age Problems | MCQ in Work Problems | MCQ in Mixture Problems | MCQ in Digit Problems | MCQ in Motion Problems | MCQ in Clock Problems | MCQ in Variation | MCQ in Progression | MCQ in Miscellaneous Problems

#### Continue Practice Exam Test Questions Part 4 of the Series

Choose the letter of the best answer in each questions.

151. 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 the water in the tank?

A. 7 hours

B. 6 hours

C. 7 1/2 hours

D. 6 1/2 hours

Solution:

152. 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. 2.75 hours

Solution:

153. A tank is filled with an intake pipe in 2 hours and emptied 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

Solution:

154. A tank can be filled in 9 hours by one pipe, 12 hours by second pipe and can be drained when fully by a third pipe in 15 hours. How long will it take to fill an empty tank with all pipes operation?

A. 7 hrs and 12 mins.

B. 7 hrs and 32 mins.

C. 7 hrs and 42 mins.

D. 7 hrs and 50 mins.

Solution:

155. If A can do the work in โxโ days and B in โyโ days, how long will they finish the job working together?

A. (x + y)/xy

B. (x + y)/2

C. (xy)/(x + y)

D. Sqrt(x)

Solution:

156. 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 Pedro to paint the same fence if he had to work alone?

A. 6

B. 8

C. 10

D. 12

Solution:

157. Glenn can paint a house in 9 hours while Stewart can paint the same house in 16 hours. They work together for 4 hours. After 4 hours, Stewart left and Glenn finished the job alone. How many more days did it take Glenn to finish the job?

A. 2.75 hours

B. 2.50 hours

C. 2.25 hours

D. 3.00 hours

Solution:

158. It takes Butch twice as long as it takes Dan to do a certain piece of work. Working together they can do the work in 6 days. How long would it take Dan to do it alone?

A. 9 days

B. 10 days

C. 11 days

D. 12 days

Solution:

159. A and B working together can finish painting a house in 6 days. A working alone can finish it in 5 days less than B. How long will it take each of them to finish the work alone?

A. 8, 13

B. 10, 15

C. 6, 11

D. 7, 12

Solution:

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

A. 19

B. 17

C. 21

D. 15

Solution:

161. It takes Myline twice as long as Jeana to do a certain piece of work. Working together, they can finish the work in 6 hours. How long could it take Jeana to do it alone?

A. 9 hours

B. 18 hours

C. 12 hours

D. 14 hours

Solution:

162. Mike, Loui and Joy can mow the lawn in 4, 6 and 7 hours respectively. What fraction of the yard can they mow in 1 hour if they work together?

A. 47/84

B. 45/84

C. 84/47

D. 39/60

Solution:

163. A farmer can plow the field in 8 days. After working for 3 days, his son joins him and together they plow the field in 3 more days. How many days will it require for the son to plow the field alone?

A. 10

B. 11

C. 12

D. 13

Solution:

164. Crew no.1 can finish installation of an antenna tower in 200 man-hour while Crew no.2 can finish the same job in 300 man-hour. How long will it take both crews to finish the same job, working together?

A. 100 man-hour

B. 120 man-hour

C. 140 man-hour

D. 160 man-hour

Solution:

165. On one job, two power shovels excavate 20,000 cubic meters of earth, the larger shovel working 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each remove 1 hour working alone?

A. 169.2, 287.3

B. 178.3, 294.1

C. 173.9, 347.8

D. 200.1, 312.4

Solution:

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

A. 19.55%

B. 22.15%

C. 27.05%

D. 25.72%

Solution:

167. 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 in order to produce a mixture of 60 cubic meters that contain 40% alcohol?

A. 20 m^3 of solution w/ 35% alcohol, 40 m^3 of solution w/ 50% alcohol

B. 50 m^3 of solution w/ 35% alcohol, 20 m^3 of solution w/ 50% alcohol

C. 20 m^3 of solution w/ 35% alcohol, 50 m^3 of solution w/ 50% alcohol

D. 40 m^3 of solution w/ 35% alcohol, 20 m^3 of solution w/ 50% alcohol

Solution:

168. 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

Solution:

169. Two thousand (2000) kg of steel containing 8% nickel is to made by mixing a steel containing 14% nickel with another containing 6% nickel. How much of each is needed?

A. 1500 kg of steel w/ 14% nickel, 500 kg of steel w/ 6% nickel

B. 750 kg of steel w/ 14% nickel, 1250 kg of steel w/ 6% nickel

C. 500 kg of steel w/ 14% nickel, 1500 kg of steel w/ 6% nickel

D. 1250 kg of steel w/ 14% nickel, 750 kg of steel w/ 6% nickel

Solution:

170. How much water must be evaporated from 10 kg solution which has 4% salt to make a solution of 10% salt?

A. 4 kg

B. 5 kg

C. 6 kg

D. 7 kg

Solution:

171. If a two digit number has x for its unitโs digit and y for its tenโs digit, represent the number

A. 10x + y

B. 10y + x

C. yx

D. xy

Solution:

172. One number is 5 less than the other. If their sum is 135, What are the numbers?

A. 85, 50

B. 80, 55

C. 70, 65

D. 75,60

Solution:

173. Ten less than four times a certain number is 14. Determine the number.

A. 6

B. 7

C. 8

D. 9

Solution:

174. The sum of 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

Solution:

175. 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

Solution:

176. Find the fraction such that if 2 is subtracted from its terms becomes 1/4, but if 4 is added to its terms it becomes 1/2.

A. 3/5

B. 5/12

C. 5/14

D. 6/13

Solution:

177. 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

Solution:

178. If 3 is subtracted from the numerator of a certain fraction, the value of the fraction became 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

Solution:

179. 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

Solution:

180. 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

Solution:

181. The tensโ digit of a number is 3km than the units โ, 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

Solution:

182. 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

Solution:

183. 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

Solution:

184. A boat man rows to a place 4.8 miles with the stream and back in 14 miles with the stream in the same time as 3 mile against the stream.

A. 1.5 mile per hour

B. 1 mile per hour

C. 0.8 mile per hour

D. 0.6 mile per hour

Solution:

185. A man rows downstream at the rate 5 mph and upstream at the rate of 2 mph. How far downstream should he go if he is to return 7/4 hours after leaving?

A. 2.5 miles

B. 3.3 miles

C. 3.1 miles

D. 2.7 miles

Solution:

186. An airplane flying the wing, 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

C. 70

D. 40

Solution:

187. A boat travels downstream in 2/3 of the time as it goes going upstream. If the velocity of the riverโs current is still water.

A. 40 kph

B. 50 kph

C. 30 kph

D. 60 kph

Solution:

188. Two planes level Manila for a southern city, a distance of 900km. Plane A travels as a ground speed of 90 kph faster than the plane B. Plane A arrived in their destination 2 hours and 15 min ahead a plane B. What is the ground speed of plane A?

A. 205 kph

B. 315 kph

C. 20 kph

D. 287 kph

Solution:

189. A train, an hour after starting, meets with accidents which detain it an hour, after which if proceeds at 3/5 of its former rate and arrives three hour after time; but had the accident happened 50 miles farther on the line, it would have arrived a one and one-half hour sooner. Find the length of the journey.

A. 910/9 miles

B. 800/9 miles

C. 920/9 miles

D. 850/9 miles

Solution:

190. On a certain trip, Edgar drive 231 km in exactly the same time as Erwin drive 308 km. If Erwinโs rate exceeded that of Edgar by 13 kph, determine the rate Erwin.

A. 39 kph

B. 44 kph

C. 48 kph

D. 52 kph

Solution:

191. In how many minutes after 2 oโclock will the hands of the clock extend in opposite directions for the first time?

a. 42.4 minutes

b. 42.8 minutes

c. 43.2 minutes

d. 43.6 minutes

Solution:

192. In how many minutes after 7 oโclock will the hands be directly opposite each other for the first time?

a. 5.22 minutes

b. 5.33 minutes

c. 5.46 minutes

d. 5.54 minutes

Solution:

193. What time after 3 oโclock will the hands of the clock be together for the first time?

a. 3:02.30

b. 3:17.37

c. 3:14.32

d. 3:16.36

Solution:

194. At what time after 12:00 noon will the hour hand and minute hand of the clock first form an angle of 1200?

a. 12:18.818

b. 12:21.818

c. 12:22.818

d. 12:24.818

Solution:

195. At what time between 8 and 9 oโclock will the minute hand coincide with the hour hand?

a. 8:42.5

b. 8:43.2

c. 8:43.6

d. 8:43.9

Solution:

196. A man left his home at past 3:00 oโclock PM as indicated in his wall clock, between 2 to 3 hours after, he returns home and noticed the hands of the clock interchanged. At what time did the man leave his home?

a. 3:31.47

b. 3:21.45

c. 3:46.10

d. 3:36.50

Solution:

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

a. 60ยฐ

b. 90ยฐ

c. 180ยฐ

d. 540ยฐ

Solution:

198. A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced by 50% of its original value at the end of 2 days, how long will it take to reduce the charge to 25% of its original charge?

a. 3

b. 4

c. 5

d. 6

Solution:

199. The resistance of a wire varies directly with its length and inversely with its area. If a certain piece of wire 10 m long and 0.10 cm in diameter has a resistance of 100 ohms, what will its resistance be if it is uniformly stretched so that its length becomes 12 m?

a. 80

b. 90

c. 144

d. 120

Solution:

200. Given that โwโ varies directly as the product of โxโ and โyโ and inversely as the square of โzโ and that w = 4 when x = 2, y = 6 and z = 3. Find the value of โwโ when x = 1, y = 4, and z = 2.

a. 3

b. 4

c. 5

d. 6

Solution:

### Online Questions and Answers in Algebra and General Mathematics Series

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

MCQ in Algebra and General Mathematics
PART 1: MCQ from Number 1 โ 50                               Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                          Answer key: PART 2
PART 3: MCQ from Number 101 โ 150                        Answer key: PART 3
PART 4: MCQ from Number 151 โ 200                         Answer key: PART 4
PART 5: MCQ from Number 201 โ 250                         Answer key: PART 5
PART 6: MCQ from Number 251 โ 300                         Answer key: PART 6
PART 7: MCQ from Number 301 โ 350                         Answer key: PART 7
PART 8: MCQ from Number 351 โ 400                         Answer key: PART 8
PART 9: MCQ from Number 401 โ 450                         Answer key: PART 9
PART 10: MCQ from Number 451 โ 500                        Answer key: PART 10

### Online Questions and Answers in Fundamentals in Algebra Series

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

MCQ in Fundamentals in Algebra
PART 1: MCQ from Number 1 โ 50                           Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                      Answer key: PART 2

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