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Q1. 25 x (-99) can be written as

• 1) 25 x (100) + 25 x 1
• 2) 25 x  (100) - 25 x 1
• 3) 25 x  (-100) - 25 x 1
• 4) 25 x (-100) + 25 x 1

Solution

Q2. (-5) x (-7) =

• 1) 36
• 2) -12
• 3) -35
• 4) 35

Solution

As the product of two negative integers is a positive integer, we have (-5) x (-7) = 35

Q3. Simplify {-13 - (-27)} + {-25 - (-40)}

Solution

{-13 - (-27)} + {-25 - (-40)} = {-13 + 27} + {-25 + 40} = {14} + {15} = 14 + 15 = 29

Q4. A cooling machine requires that room temperature to be lowered from 50^oC at the rate of 5^oC every hour. What will be the room temperature after 8 hours of starting the process?

Solution

Room temperature at the beginning of the process = 50^oC Rate of lowering the temperature = 5^oC every hour Temperature lowered after 8 hours= 5 × 8 = 40^oC Room temperature after 8 hours = 50^oC - 40^oC = 10^oC

Q5. Shabana goes 30 Km north from a point P to the point Q. She moves 45 km towards South along the same road. If the distance towards north is represented as positive integer, then how will you represent the distance travelled towards south? Which integer would be represented as her final position?

Solution

Distance towards north (positive) = +30 Km Distance towards south (negative) = -45 Km Final Position = 30 + (-45) = 30 - 45 = -15 Km

Q6. A frog jumps 3 steps forward and then 5 steps backward starting from the point zero on the number line. What is the present position of frog?

• 1)
• 2)
• 3)
• 4)

Solution

Three steps forward from zero would take the frog to the point +3.Then 5 steps backward would take the frog to -2Hence present position of frog is -2.

Q7. -5 + 9 + (-5) + (-10) + (1) is equal to

• 1) -10
• 2) -13
• 3) 10
• 4) 13

Solution

-5 + 9 + (-5) + (-10) + (1) -5 + 9 = 44 + (-5) = -1-1 + (-10) = -1 - 10 = -11-11 + 1 = -10So, -5 + 9 + (-5) + (-10) + (1) = -10

Q8. [(-45) 5][(-3) + (-6)] + [(-7) (2)]

• 1) 8
• 2) -13
• 3) 13
• 4) -18

Solution

[(-45) 5][(-3) + (-6)] + [(-7) (2)] = [-9] [-9] + [-14]= 1 + (-14)= -13

Q9. A scientist cools two samples of bacteria to see effect of temperature on two samples. He cools one sample to -53^oC and the other to -42^oC in the laboratory. Which sample is colder and by how much?

Solution

The temperature to which first sample is cooled = -53^oCThe temperature to which second sample is cooled = -42^oCSince -53^oC < -42^oC                So the first sample is colder than the second one.                                                        And, temperature difference = -53 - (-42) = -53 + 42 = -11°C                                                   

Q10. The arrangement of integers 20, -1, 0, -5, -21, -9 in ascending order is

• 1) 0, 20, -1, -9, -5, -21
• 2) 20, -9, 0, -1, -5, -21
• 3) -21, -9, -5, -1, 0, 20
• 4) -5, 0, -1, -21, 20, 9

Solution

Ascending order means arranging the numbers from smallest to highest.Smallest number is the highest negative number, which is -21.Then the highest negative number from the remaining numbers is -9Then -5 followed by -1.0 is greater than negative numbers and smaller than positive numbers.The highest number is 20.So the arrangement in ascending order is -21, -9, -5, -1, 0, 20

Q11. A Chemical is unstable at room temperature, so it is kept in a refrigerator at -38^oC. Once removed from the fridge, its temperature rises at a rate of 4^oC per minute. Assuming a bottle of the chemical was exactly -38^oC when removed from the fridge, what will its temperature be five minutes after removal from the fridge?

Solution

The temperature at which the chemical is stored = -38^oC        The rate of rise of temperature after the sample is removed from refrigeration= 4^oC per minute                                                        Rise in temperature after 5 minutes = 4x5 = 20^oC                         Net temperature of the chemical after 5 minutes = -38 + 20                                                                              =  -18^oC

Q12. In an exam involving negative marking, the maximum marks scored were 75 out of 100 and minimum marks scored were -6. How many marks less is the minimum marks from the maximum marks?

• 1) 91
• 2) -6
• 3) -16
• 4) 81

Solution

Maximum marks = 75Minimum marks = -6Difference between two marks = 75 - (-6) = 75 + 6 = 81So -6 is 81 marks less then 75

Q13. Why the product (-9) × (-5) × (-6) is negative, while (-9) × (-5 )× (-6) × (-1) is positive? Give reason.

Solution

When odd number of negative integers is multiplied, the result is a negative integer. So, (-9) × (-5) × (-6) = -270 When even number of negative integers is multiplied, the result is a positive integer. So, (-9) × (-5 ) × (-6) × (-1) = 270

Q14. [(-224) 32][(-25)(-5)]+[(-5)2] ......

• 1) -70
• 2) 45
• 3) 10
• 4) -45

Solution

[(-224) 32] [(-25) (-5)] + [(-5) 2]= [-7] [5] + [-10]= [-35] + [-10]= -35 - 10= -45         

Q15. A Poultry farm produces 600 eggs every week and delivers them equally to 10 shops. The shopkeepers charge Rs.5 for every good egg but they have to give Rs.2 to the customer if the egg comes out to be rotten. A shopkeeper could only earn Rs.276 despite selling all the eggs. How many eggs were rotten?

Solution

Eggs produced by the poultry farm = 600 Eggs delivered to each shop = 600  10 = 60 Money earned by a particular shopkeeper = Rs. 276 Money earned if all eggs were good = 60 × 5 = Rs. 300 Money lost due to rotten eggs = 300 - 276 = Rs. 24 Cost that shopkeeper will give for one rotten egg = Rs. 2 Number of rotten eggs = 24 2 = 12Hence, 12 eggs were rotten.

Q16. Ritu and her 3 friends are having a pizza party. They decided to share the bill equally among themselves. If the bill price is Rs. 460, then what will be each one's contribution to bill?

Solution

Total number of persons = 4 Bill amount to be given = -460 Thus, each one's constribution = (-460) 4 = -115 Hence, each one has to pay Rs. 115.