# 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.