Important Questions for Class 8 Chapter 8-Comparing Quantities

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Important questions based on NCERT syllabus for Class 7 Class 8 Chapter 8 - Comparing Quantities:

Question 1: A number is increased by 10% and then it is decreased by 10%. Find the net increase or decrease percent.
Solution:
Let the number be 100
Increase in the number = 10% = 10% of 100 = 10
∴ Increased number = 100 + 10 = 110
This number is decreased by 10%
∴ Decrease in the number
=10%=10% of 110=(10/100 × 100) = 11
∴ New number = 110 - 11 = 99
Thus, net decrease = 100 - 99 = 1
Hence net percentage decrease
=(1/100 × 100)% = 1%

Question 2: A toy was sold at a gain of 12%. Had it been sold for Rs. 33 more, the gain would have been 14%. Find the cost price of the toy.
Solution:
Let the C.P. of the toy be Rs. x
Gain% = 12%
∴ Gain = 12% of Rs.x = Rs.12x/100 = Rs.3x/25
∴ S.P. = C.P. + Gain
= Rs.(x + 3x/25) = Rs. 28x25
New Gain % = 14%
∴ New Gain = 14% of Rs.x = Rs. 14x/100 = Rs. 7x/50
∴ New S.P. = Rs. (x+7x/50) = Rs57x/50
∴ 57x/50 − 28x/25 = 33
⇒ 57x − 56x/50 = 33
⇒ x/50 = 33
⇒ x = 33 × 50
⇒ x = 1650
Hence, the C.P. of the toy is Rs. 1650

Question 3: Amit purchases a motorcycle, having marked price Rs. 46000 at a discount of 5%. If VAT is charged at the rate of 10%, find the amount Amit has paid to purchase the motorcycle.
Solution:
Marked price of motorcycle = Rs. 46000
Discount = 5% of Rs. 46000
=Rs. (5/100 × 46000) = Rs. 2300
∴ Net price of motorcycle = Rs. 46000 - Rs.2300 = Rs.43700
VAT = 10% of Rs.43700 = Rs.(10/100 × 43700) = Rs. 4370
∴ S.P. of motorcycle = Rs.(43700 + 4370) = Rs.48070
Hence, Amit has paid Rs.48070 to purchase the motorcycle.