Question

1. a. In an examination, 60 candidates sat for either Mathematics or English language 20% passed in Mathematics only and 40% passed in English language only. If each candidate passed in at least one of the subjects, how many candidates passed in i. Mathematics ii. English language? b. Illustrate the information given in (a) on a Venn diagram c. Daddy had GH¢50.00 in his pocket. He gave half of the amount to Mama; he also gave GH€10 to the house boy later. What fraction of the amount was left on him? 2. a. i. Find the width of a cuboid with height 8m and length 12m, given that the volume is 480m ii. Calculate the total surface area of the cuboid b. Find the truth set of: 1 - m + m -3 = 6 5 4​

Answer 1

• The number of students who Passed mathematics is 36 and the number who passed English is 48

• The fraction of the amount left to Daddy is 3/10

• The width of the cuboid is 5 meter and it's surface area is 380 meter

A.)

Total Number of students = 60

Since each candidate passed in atleast one of English and Math ; the none of the students failed.

Percentage who passed :.

Mathematics only = 20%

English only = 40%

Since, no one failed ; percentage that passed both = 100% - (40+20)% = 40%

Number who passed Mathematics only :

20% × 60 = 12 students

Number that passed English only :

40% × 60 = 24 students.

Number that passed both = (40% × 60) = 24 students

Number that passed English = (Number that passed English only + Number that passed both) = 24 + 24 = 48

.Number that passed mathematics = (Number that passed Maths only + Number that passed both) = 12 + 24 = 36

2.)

Total daddy has = 50

Half given to mummy = 1/2 × 50 = 25

Amount given to houseboy = 10

Amount left = 50 - (25 + 10) = 15

Fraction of Amount left = 15/50 = 3/10

C.)

Length of cuboid = 12

Height = 8 cm

Volume of cuboid = 480

Width = w

Recall :

Volume = Length × width × height

480 = 12 × 8  × w

480 = 96w

w = 490 / 96

w = 5

Width of the cuboid = 5

The surface area of a cuboid : 2(lh + lw + hw)

Hence,

2([(12×8) + (12×5) + (8 ×5)]

2(96 + 60 + 40)

2(190)

380 m

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