8th Grade > Mathematics
COMPARING QUANTITIES MCQs
:
A
A=P×[1+r100]n, where P is the principal, r is the rate of interest and n is the time period.
C.I = A - P
Here, P = ₹ 20,000, r = 10 %, and n = 3 years
A=20,000×[1+10100]3
A=20,000×[11×11×1110×10×10]
A = ₹ 26,620
So, C.I = 26,620 - 20,000 = ₹ 6,620
:
B
The price hike is 10%. So, 10% of 42,00,000 would give you the price hike.
Hence, 10100×42,00,000=4,20,000
So, adding this amount to the previous price i.e. 42 lakhs would give you the new price.
So, 42,00,000 + 4,20,000 = ₹ 46,20,000
:
B
As the selling price is less than the cost price, the owner incurred loss.
Loss = Difference in the amount for which it was purchased and the amount for which it was sold.
∴Loss=₹ 80000−₹ 60000 =₹ 20000
Percentage of loss=losscost price×100
=2000080000×100=25%
:
B
Given: Out of total population, 25% were doctors, 30% engineers, 15% businessmen and rest were illiterates.
Hence, percentage of illiterates =100−(25+30+15)=30%
So, number of illiterates =30% of 5000
=30100×5000
=1500
:
A
Fraction of apples =Number of applesTotal number of fruits in the bag
So, fraction of apples =1030=13
:
B
Profit on one of the bats = 10% of ₹ 6000
= 10100×6000= ₹600
Hence, the Selling price
= Cost price + Profit
= ₹ (6000 + 600) = ₹ 6600
Loss on the other bat
= 5% of ₹ 6000
= 5100×₹ 6000
= ₹ 300
Selling price = Cost price - Loss
= ₹ (6000 - 300)
= ₹ 5700
Total cost price (CP) = ₹ 12000
Total selling price (SP) =₹6600+₹5700 = ₹ 12,300
Hence, as SP > CP, he has made a profit of ₹ (12,300−12,000) = ₹ 300.
:
D
Given that P = ₹ 64,000 r = 5 % and n = 112 years
Since, the rate of interest is calculated annually , for 6 months it will be 2.5 %
A=P(1+r100)n
Here r = 52 % and n = 3 half years
A=64,000(1+52×100)3
A=64,000(4140)3
A=68921
∵ Compound interest = Amount - Principal
= 68921 - 64000
= ₹ 4921
:
A
When a principal is promised with an interest to be compounded annually, the amount after one year becomes the principal for the next year. So, 10100×400000=40,000
₹40,000 added to ₹4,00000 would be the new principal for the next year i.e. 4,40,000. The interest for the second year is calculated on the new principal amount: 10100×440000×1=44,000
So, the final amount after 2 years(compounded annually with 10% interest) = ₹440000 + 44000 = ₹4,84,000.
If the principal would have been deposited for an annual simple interest for 10% for a period of two years would be 10100×400000×2=80,000
Therefore amount = ₹4,00000 + ₹80,000 = ₹4,80,000.
So, compound interest is ₹4,000 more than a simple interest for a period of two years.
:
A
GST is calculated on the selling price. Since the bill amount is the selling price, the GST is added to the bill amount itself.
So, GST = 4% of ₹ 3000
= 4100×3000
= ₹ 120
Final bill amount = ₹3000 + ₹ 120 = ₹ 3120
:
A, B, and D
For a sum whose interest is calculated by compounding, the following things need to be defined:
-Principal
-Rate of interest
-Conversion periods (annual, half-yearly)
The time taken to return the loan is not fixed. Based on the time taken and the other fixed details above, the final interest is calculated.