# Standard Mathematics Questions, Explanation and Detailed Step-By-Step Solutions For J.H. S and B.E.CE Candidates.

Mathematics is a core subject in the Junior High School Curriculum. Below are sample step-by-step standard Mathematics questions, explanation and detailed step by step solutions for J.H. S and B.E.CE candidates to pass with ease. The questions can be used as both objectives and theory ( Section B). This is because I have provided detailed solution for each question for students easy understanding.

(1) A car was supposed to cover a distance of 320km but it broke down half-way. The uncovered distance of the car will be…….

A. 320.5km

B. 480km

C. 160km

D. 160.5km

Correct answer is C

Explanation: With a question like this, multiply half by the total distance expected to be covered by the car subtract the result from the total distance to be covered to get the uncovered distance.

Solution

Distance to be covered = 320km

Broke down distance= 1/2 the total distance

=> 1/2×320

=> 320/2

=> 160km

Therefore, the car broke down half-way at 160km.

To get the uncovered distance, subtract the distance covered when the car broke down half-way from the total distance expected to be covered by the car.

Uncovered distance= 320km-160km

=> 160km hence, the correct answer is option C

(2) There are 200 people in a theatre. 30 of them are kids and the rest of them are adults. What fraction of the total number of people there represent adults?

A. 17/20

B. 3/20

C. 1/20

D. 7/20

Correct answer is A

Explanation: Given the total number of people, 200 and 30 of them being kids, the number of adults is calculated by subtracting the number of kids from the total number of people at the theatre. Afterwards, divide the number of adults by the total number of people to get the fraction of people in the theatre who are adults.

Solution

Total number of people = 200

Number of kids= 30

Number of adults = Total number of people – Total number of kids

=> 200-30

=> 170

Fraction of adults = Total number of adults / Total

number of people

=> 170/200 cancel out

=> 17/20 hence, the correct answer is A

(3) There are 70 students in General Arts class. If 12 students study Economics and Geography, what fraction of the total number of students in the class represent these students ?

A. 35/6

B. 6/35

C. 5/36

D. 3/70

Correct answer is B

Explanation: Given the total number of students , 70 and the number of students who study Economics and Geography, 12, divide the number of students who study Economics and Geography by the total number of students in the class to get the fraction they represent in the class.

Solution

Total number of students = 70

Students who study Economics and Geography = 12

Fraction of students who study Economics and Geography = Number of students who study Economics and Geography / Total number of students in the class

=> Fraction= 12/70 cancel out

=> 6/35 hence, the correct answer is B

(4) About 40% of people in a community are literates. If there are 700 people in the community, what fraction of the total number of people in the community are illiterates?

A. 2/5

B. 3/5

C. 4/5

D. 1/5

Correct answer is B

Explanation: To begin, you first find the number of people who are literates with the given percentage. Afterwards, subtract your result from the total number of people in the community to get the number of people which is700 in the community who are illiterates. You then divide you result by the total number of people in the community to get the fraction they represent.

Solution

Total number of people in the community = 700

Fraction of literates = 40%

Number of liberated = Fraction of liberated × Total number of people

=> 40% × 700 but 40% = 40/100

=> 40/100 ×700

=> 40×700/100

=> 28000/100 cancel out by dividing by 100

=> 280 literates

Number of illiterates= Number of people in the community – Number of liberates

=> 700-280

=> 420 illiterates

Fraction of illiterates= Number illiterates/ Total number of people in the community

=> 420÷700 = 420/700 cancel out

=> 42/70 = 3/5

Therefore, 3/5 of the people in the community are illiterates hence, the correct answer is B.

(5) In a congregation of 900 women, five- sixth are not married. What fraction of the total number of women are married?

A. 7/12

B. 1/12

C. 5/6

D. 1/6

Correct answer is D

Explanation: With the given total number of women which is 900 and the fraction of it married which is 5/6, proceed to calculate the number of women who are not married and subtract it is from the total number of women to get the number of married women. Afterwards, divide the number of married women by the total number of women to get the fraction they represent.

Solution

Total women = 900

Fraction of not married = 5/6

Number of not married women= Fraction of not married × Total number of women in the congregation

=> 5/6 × 900

=> 5×900/6

=> 4500/6

=> 750

Married women= Total women – Total unmarried women

=> 900-750

=> 150

Fraction of married women= Number of married women ÷ Total number of women => 150÷900 = 150/900 cancel out

=> 15/90

=> 1/6

Therefore, the fraction of married women is equal to 1/6 hence, the correct answer is option D.

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