Comparing Quantities Test

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Comparing Quantities Test - 55

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Weekly Quiz Competition

Question 1
1 / -0

Suppose for the principal $$P$$, rate $$R\%$$ and time $$T$$ years the simple interest is $$S$$ and compound interest is $$C$$. Consider the possibilities :
(i) $$C > S$$ (ii) $$C = S$$ (iii) $$C < S$$

Which of the following options hold?

A
Only (i) is correct.

B
Either (i) or (ii) is correct

C
Either (ii) or (iii) is correct

D
Only (iii) is correct.

Solution

Case 1. $$C> S$$
This is possible if interest is compounded quarterly or half-yearly.
Case 2. $$C=S$$
This is possible if interest is compounded yearly.
Case 3. $$C<S$$
It can not be true because simple interest cannot be greater than compound interest.
Hence, Option B is correct option.
Question 2
1 / -0

Jogen's taxable income for $$2010-11$$ is Rupees $$5,00,000$$. The tax rates are (i) nil for first $$1,50,000$$, (ii) $$10\%$$ for $$1,50,001$$-$$3,00,000$$ and (iii) $$20\%$$ for the remaining. His Tax liability is:

A
Rs $$45000$$

B
Rs $$50000$$

C
Rs $$55000$$

D
Rs $$60000$$
Question 3
1 / -0

The cost of a vehicle is Rs. $$1,75,000$$. If its value depreciates at the rate of $$20\%$$ per annum, then the total depreciation after $$3$$ years was _________.

A
Rs. $$86,400$$

B
Rs. $$82,500$$

C
Rs. $$84, 500$$

D
Rs. $$85,400$$

Solution

Cost of vehicle $$= 175000$$
Depreciation for first year $$= \dfrac{20}{100}\times175000=35000$$

Cost of vehicle after first year $$= 175000-35000=140000$$
Depreciation for second year $$= \dfrac{20}{100}\times140000 = 28000$$

Cost of vehicle after second year $$= 140000-28000=112000$$
Depreciation for third year $$= \dfrac{20}{100}\times112000 = 22400$$

Total depreciation after $$3$$ years $$= 35000+28000+22400 = 85400$$
Hence, the answer is Rs. $$85,400$$.
Question 4
1 / -0

A shopkeeper sold an article for $$\text{Rs. } 2090.42$$ without any loss or profit. Approximately, what will be the profit percent, if he sells that article for $$\text{Rs. }2602.58$$?

A
$$15\%$$

B
$$20\%$$

C
$$25\%$$

D
$$30\%$$

Solution

Selling price of an article without any loss or profit $$=\text{Rs. } 2090.42$$
$$\therefore$$ Cost price $$=\text{Rs. } 2090.42$$
New selling price $$=\text{Rs. } 2602.58$$
Profit $$=S.P - C.P. = \text{Rs. }2602.58 - \text{Rs. } 2090.42 $$
$$=\text{Rs. } 512 .16$$
$$\therefore\text{Profit} \%=\dfrac{\text{Profit}}{C.P} \times 100 = \dfrac{512.16}{2090.42}\times 100$$
$$\simeq 25\%$$ (approx)
Question 5
1 / -0

Kabir buys an article with $$25\%$$ discount on its marked price. He makes a profit of $$10\%$$ by selling it at Rs. $$660$$. The marked price is ___________.

A
Rs. $$600$$

B
Rs. $$700$$

C
Rs. $$800$$

D
Rs. $$685$$

Solution

let the marked price is Rs. $$x$$
the price for which he bought $$=(1-.25)\times x=0.75x$$
he sells it at $$660$$ and makes a profit of $$10\%$$

$$\dfrac{660-0.75x}{0.75x}=0.1$$
$$660-0.75x = 0.075x$$
$$660=0.825x$$
$$x=800$$
Question 6
1 / -0

The value of a car depreciates every year at the rate of 10% on its value at the beginning of the year. If the present value of the car is Rs 52,488 its worth four years ago was

A
$$Rs\ 68.232$$

B
$$Rs\ 68.234$$

C
$$Rs\ 69.862$$

D
$$Rs\ 80,000$$

Solution

Present Value $$A= Rs.52,488$$
Depreciation rate $$r = 10\%$$ per annum
Time $$t = 4$$ years
Let initial value be $$ P $$
We know the formula, $$\displaystyle A=P(1-\dfrac{r}{100})^t$$
Substituting the given values, we get.
$$52,488 = P[1-\dfrac{10}{100}]^4$$
$$52,488 = P(0.9)^4$$
$$P=\dfrac{52488}{0.6561}$$
$$P = Rs. 80,000$$
Question 7
1 / -0

A man earns Rs. $$20$$ on the first day and spends Rs. $$15$$ on the next day. He again earns Rs. $$20$$ on the third day and spends Rs. $$15$$ on the fourth day. If he continues to save in this way, how soon will he have Rs. $$60$$ in hand?

A
On $$12$$th day

B
On $$24$$th day

C
On $$17$$th day

D
On $$27$$th day

Solution

In two days saving $$=$$Rs. $$5$$
Saving in $$16$$ days $$=$$ Rs. $$40$$
Income on $$17$$th day $$=$$Rs. $$60$$
Inhand on $$17$$th day $$=$$Rs. $$60$$.
Question 8
1 / -0

A shopkeeper mixes two varieties of Tea, one costing Rs. $$40$$/kg and another Rs. $$50$$/kg in the ratio $$3:2$$. if he sells the mixed variety of Tea at Rs. $$48$$/kg, his gain or loss percent is

A
$$48.4$$% gain

B
$$48.4$$% loss

C
$$10$$% gain

D
$$10$$% loss

Solution

Average CP of Mixed Tea when Mixed in Ratio $$3:2$$
$$=\cfrac { 40\times 3+50\times 2 }{ 3+2 } =\cfrac { 220 }{ 5 } =Rs.44$$
Wen SP=Rs. $$48/kg$$
$$=\cfrac { 4 }{ 44 } \times 100=9.09\approx 10$$% gain
Question 9
1 / -0

A shirt was sold at a profit of 15$$\%$$. If its cost had been 5$$\%$$ less and it had been sold for Rs. 21 less, then the profit would have been 10$$\%$$. Find the cost of the shirt.

A
$$Rs.\ 210$$

B
$$Rs.\ 220$$

C
$$Rs.\ 100$$

D
$$Rs.\ 200$$

Solution

Given that:
A shirt was sold at a profit of $$15\%$$.
If the cost had been $$5\%$$ less, and it had been sold for $$Rs.\ 21$$ less, then the profit would have been $$10\%$$.

To find out:
The cost of the shirt.

Let the cost of the shirt be $$Rs.\ x$$.
We know that, $$S.P.=\dfrac{(profit\%+100)C.P.}{100}$$
Here, $$profit\%=15$$

$$\therefore\ S.P.=\dfrac{(15+100)x}{100}\\$$
$$\Rightarrow S.P.=1.15x\\$$

Now, if the cost is $$5\%$$ less, then,
$$C.P.=95\%\ of\ x\\$$
$$\Rightarrow C.P.=\dfrac{95}{100}x\\$$
$$\therefore \ C.P.=0.95x\\$$
Also, the selling price is $$Rs. \ 21$$ less.
$$\therefore\ S.P.=1.15x-21\\$$
In this case, the profit would have been $$10\%$$, as given in the problem.

Now, we know that, $$profit\%=\dfrac{S.P.-\ C.P.}{C.P.}\times 100$$

$$\therefore \ 10=\dfrac{(1.15x-21)-0.95x}{0.95x}\times 100\\$$
$$\Rightarrow 10=\dfrac{1.15x-21-0.95x}{0.95x}\times 100\\$$
$$\Rightarrow 10\times 0.95x=(0.20x-21)\times 100\\$$
$$\Rightarrow 9.5x=20x-2100\\$$
$$\Rightarrow 20x-9.5x=2100\\$$
$$\Rightarrow 10.5x=2100\\$$
$$\Rightarrow x=\dfrac{2100}{10.5}\\$$
$$\therefore \ x=Rs.\ 200\\$$

Hence, the cost of the shirt is $$Rs.\ 200$$.
Question 10
1 / -0

Publisher sells books to retailer at marked price which is $$20$$% above his outlay. If on cash payment, he allows a discount of $$10$$% go the marked price. The publisher thus gains

A
$$12$$%

B
$$10$$%

C
$$8$$%

D
$$14$$%

Solution

Let CP of Book $$=100$$
MP$$=120$$
SP after Discount $$=\cfrac { 90 }{ 100 } \times 120=108$$
Profit $$\% =8$$%

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 55

Result

Comparing Quantities Test - 55

Score

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Rank

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SHARING IS CARING

Question 1

Only (i) is correct.

Either (i) or (ii) is correct

Either (ii) or (iii) is correct

Only (iii) is correct.

Solution

Question 2

Rs $$45000$$

Rs $$50000$$

Rs $$55000$$

Rs $$60000$$

Question 3

Rs. $$86,400$$

Rs. $$82,500$$

Rs. $$84, 500$$

Rs. $$85,400$$

Solution

Question 4

$$15\%$$

$$20\%$$

$$25\%$$

$$30\%$$

Solution

Question 5

Rs. $$600$$

Rs. $$700$$

Rs. $$800$$

Rs. $$685$$

Solution

Question 6

$$Rs\ 68.232$$

$$Rs\ 68.234$$

$$Rs\ 69.862$$

$$Rs\ 80,000$$

Solution

Question 7

On $$12$$th day

On $$24$$th day

On $$17$$th day

On $$27$$th day

Solution

Question 8

$$48.4$$% gain

$$48.4$$% loss

$$10$$% gain

$$10$$% loss

Solution

Question 9

$$Rs.\ 210$$

$$Rs.\ 220$$

$$Rs.\ 100$$

$$Rs.\ 200$$

Solution

Question 10

$$12$$%

$$10$$%

$$8$$%

$$14$$%

Solution

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