Solved Questions on Integers
1. A number changes from −30 to 55. What is the increase or decrease in the number?
a) Increases by 75
b) Decreases by 75
c) Increases by 85
d) Decreases by 85
Answer: c) Increases by 85
Explanation: The number changes from −30 to 55 = 55 − (−30)
= 55 + 30 = 85
∴ It will be increased.
2. The product of two integers is −91.5. If one of them is 12.2, what is the other integer?
a) −5
b) −5
c) −5
d) −5
Answer: b) −7.5
Explanation: The product of two integers = −91.5
One integer = 12.2
∴ Second integer = −91.5 ÷ 12.
= −7.5
3. What is the result of the following statement?
Statement: Add the product of 9.5 and (−2.25) to the quotient of (−161) and 23.
a) 14.375
b) −37
c) 28.375
d) −375
Answer: d) −28.375
Explanation: Add the product of 9.5 and (−2.25) to the quotient of (−161) and 23.
= [9.5 × (−2.25)] + [(−161) ÷ 23)]
= (−21.375) + (−7)
= −21.375 − 7
= −28.375
4. A shopkeeper earns a profit of $2 by selling a pen and incurs a loss of 40 cents per pencil and a loss of 25 cents per eraser while selling pencils and erasers of old stock. On a particular day, he earns a profit of $10. If he sold 10 pens and the number of pencils and erasers he sold are in the ratio 5 : 12, what is the number of pencils and erasers she sold on that day?
a) 5 Pencils and 12 erasers
b) 10 Pencils and 24 erasers
c) 15 Pencils and 24 erasers
d) 15 Pencils and 36 erasers
Answer: b) 10 Pencils and 24 erasers
Explanation: By selling a pen, gain per pen = $2
By selling pencils, loss per pencil = 40 cents
By selling an eraser, loss per eraser= 25 cents
On one day, he gains = $10
On that day, he sold 10 pens and pencils and erasers in a ratio of 5 : 12
On ten pens, his gain = 10 × $2
= $20
Loss on pencils and erasers = $20 − $10 = $10 = 10 × 100 cents
= 1000 cents
Ratio in pencil and erasers = 5 : 12
Let the number of pencils be 5a and the number of erasers is 12a.
Loss on pencils and erasers = 1000 cents
⇒ 5a × 40 + 12a × 25 = 1000
⇒ 200a + 300a = 1000
⇒ 500a = 1000
⇒ a = 2
Number of pencils = 5 × a = 5 × 2 = 10
Number of erasers = 12 × a = 12 × 2 = 24
5. In a quiz, $285 is awarded for every correct answer and a penalty of $75 is put for every incorrect answer. Tesla answered 15 questions out of which only 7 answers were correct. How much money is earned by Tesla in the quiz?
a) $1395
b) $1595
c) $1795
d) $1995
Answer: a) $1395
Explanation: In a quiz, $285 is awarded for every correct answer and $75 is put as the penalty for every incorrect answer.
Tesla answered 15 questions but 7 questions were correct answers.
Number of correct answers = 7
Money earned for correct answers = 7 × $285 = $1995
Number of incorrect answers = 15 – 7 = 8
Money deducted (Penalty) for incorrect answers = $75 × 8 = $600
Money earned by Tesla in the quiz = $1995 – $600 = $1395
