Free Comparing Quantities 02 Practice Test - 8th Grade 

Depreciation means a decrease in the value due to use and age of the item.

$A=P\times {[1-\frac{r}{100}]}^n$, where $A$ is the amount, $P$ is the principal, $r$ is the rate of interest and $n$ is the time period.

So, price at the end of one year $=2,50,000\times {[1-\frac{10}{100}]}^1$= ₹ 2,25,000

Depreciation for next four months $=2,25,000\times 10\times \frac{1}{100\times 3}$ = ₹ 7500

So, the depreciated value after one year and four months $=2,25,000-7,500$ = ₹ 2,17,500

$A=P\times [1+\frac{r}{100}{]}^n$, 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

$A=20,000\times [1+\frac{10}{100}{]}^3$
$A=20,000\times \left[\frac{11\times 11\times 11}{10\times 10\times 10}\right]$
A = ₹  26,620

So, C.I = 26,620 - 20,000 = ₹ 6,620

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.

$\therefore \text{Loss}=₹80000-₹60000=₹20000$

$\text{Percentage of loss}=\frac{\text{loss}}{\text{cost price}}\times 100$ 

                                $=\frac{20000}{80000}\times 100=25\%$

Hence, $\frac{10}{100}\times 42,00,000=4,20,000$
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

Fraction of apples $=\frac{\text{Number of apples}}{\text{Total number of fruits in the bag}}$ 

So, fraction of apples $=\frac{10}{30}=\frac{1}{3}$

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
                                        $=\frac{30}{100}\times 5000$
                                        $=1500$

Profit on one of the bats = 10% of ₹ 6000
= $\frac{10}{100}\times 6000=$ ₹600

Hence, the Selling price
= Cost price + Profit
= ₹ (6000 + 600) = ₹ 6600

Loss on the other bat
= 5% of ₹ 6000
= $\frac{5}{100}\times ₹6000$
= ₹ 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.

Given that  P = ₹ 64,000  r = 5 % and n = $1\frac{1}{2}$ years

Since, the rate of interest is calculated annually , for 6 months it will be 2.5 %

$A=P(1+\frac{r}{100}{)}^n$

Here r = $\frac{5}{2}$ % and n = 3 half years

$A=64,000(1+\frac{5}{2\times 100}{)}^3$
$A=64,000(\frac{41}{40}{)}^3$
$A=68921$

$\because$ Compound interest = Amount - Principal
                                     = 68921 - 64000
                                     = ₹ 4921

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
= $\frac{4}{100}\times 3000$ 
= ₹ 120

Final bill amount = ₹3000 + ₹ 120 = ₹ 3120

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, $\frac{10}{100}\times 400000=40,000$
₹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: $\frac{10}{100}\times 440000\times 1=44,000$
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 $\frac{10}{100}\times 400000\times 2=80,000$
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.