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Questions Related to maths

Multiple choice introduction to ratio and percentages comparing quantities maths

If selling price is doubled, the profit triples. Find the profit percent.

  1. $66\dfrac {2}{3}$
  2. $100$
  3. $105\dfrac {1}{3}$
  4. $120$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C.P. be $Rs. x$ and S.P. be $Rs. y$.
Then, $3(y - x) = (2y - x) \Rightarrow y = 2x$.
$Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x$.
$\therefore Profit$ % $= \left (\dfrac {x}{x}\times 100\right )$% $= 100$%

Multiple choice introduction to ratio and percentages comparing quantities maths

Two pipes A and B can fill a tank in $15$ minutes and $20$ minutes respectively. Both the pipes are opened together but after $4$ minutes, pipe A is turned off. What is the total time required to fill the tank?

  1. $10$ min. $20$sec.
  2. $11$ min. $45$sec.
  3. $12$ min. $30$ sec.
  4. $14$ min. $40$ sec.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Part filled in $4$ minutes $=4\left(\displaystyle\frac{1}{15}+\frac{1}{20}\right)=\displaystyle \frac{7}{15}$.
Remaining part$=\left(1-\displaystyle\frac{7}{15}\right)=\displaystyle\frac{8}{15}$.
Part filled by B in $1$ minute $=\displaystyle\frac{1}{20}$
$\therefore \displaystyle\frac{1}{20}:\frac{8}{15}::1:x$
$x=\left(\displaystyle\frac{8}{15}\times 1\times 20\right)=10\displaystyle\frac{2}{3}$min$=10$ min. $40$ sec.
$\therefore$ The tank will be full in $(4$ min. $+10$ min. $+40$ sec.)$=14$min. $40$sec.

Multiple choice introduction to ratio and percentages comparing quantities maths

What is the percent profit earned by the shopkeeper on selling the articles in his shop?
I. Labeled price of the article sold was $130$% of the cost price.
II. Cost price of each article was $Rs. 550$.
III. A discount of $10$% on labeled price was offered.

  1. Only I

  2. Only II

  3. I and III

  4. All the three are required

  5. Question cannot be answer even with information in all the three statements.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I. Let C.P. be $Rs. x$.
Then, $M.P. = 130$% of $x = Rs. \left (\dfrac {13x}{10}\right )$
III. $S.P. = 90$% of M.P.
Thus, I and III give, $S.P. = Rs. \left (\dfrac {90}{100}\times \dfrac {3x}{10}\right ) = Rs. \left (\dfrac {117x}{100}\right )$
$Gain = Rs. \left (\dfrac {117x}{100} - x\right ) = Rs. \dfrac {17x}{100}$
Thus, from I and III, gain % can be obtained.
Clearly, II is redundant.

Multiple choice introduction to ratio and percentages comparing quantities maths

If the diameter of a sphere is decreased by $25\%$, by what percent does its curved surface area decrease?

  1. $43.75\%$
  2. $21.88\%$
  3. $50\%$
  4. $25\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved surface area of sphere$=4\pi r^2$
diametre after decreases by $25\%$
$A _D=\pi d^2$
$d _1=\displaystyle\frac{75}{100}d=\frac{3d}{4}$
$A _1=\pi \left(\displaystyle\frac{3d}{4}\right)^2=\frac{9}{16}\pi d^2$
$\%$ decrease=$\displaystyle\frac{\displaystyle\frac{9}{16}\pi d^2-\pi d^2}{\pi d^2}\times 100=-43.75\%$

Multiple choice maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

Round off to nearest lakhs: The given number is $38,65,62,048$

  1. $38,68,60,000$
  2. $38,65,600$
  3. $38,65,00,000$
  4. $38,66,00,000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To round of the given no in nearest lakh we need to see the value at ten thousand place which is $6$ it is more than $5$. 

So we round off lakhs digit to $5+1=6$
So we will round off. $38,65,62,048$ will become $38,66,00,000$

Multiple choice maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

Round off  $231$ to nearest $100.$

  1. $200$
  2. $300$
  3. $250$
  4. $350$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  In number $231$,tens digit is $3$ 

$\Rightarrow$  Its tens digit is 3, which is less than 5. So, we replace each of the tens and ones digits by $0$ and keep the other digits as they are to round off the given number to nearest hundreds.
$\therefore$  Round of 231 to nearest 100 is $200$.

Multiple choice maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

Round off $829$ to nearest $100$. 

  1. $800$
  2. $700$
  3. $900$
  4. $850$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  The given number is $829$

$\Rightarrow$  Its tens digit is $2$, which is less than $5$. 
$\Rightarrow$  So, we replace each of the tens and ones digits by $0$ and keep the other digits as they are to round off the given number to nearest $100.$
$\therefore$  Round off $829$ to nearest $100$ is $800$.

Multiple choice maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

Round off the following number to the nearest $10$ and $100$:
$1634$

  1. $1630,1600$
  2. $1640,1730$
  3. $1740,1700$
  4. $1640,1734$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$1634=163.4 \times  10^1$

Rounding to nearest 10, we round off $163.4$ to $163.0$ as $4$ is less than $5$

Answer: $1630$

Similarly for 100 th position 
$1634 = 16.34\times 20^2$

$16.34 = 16.30 = 16.00$

So the answer is $1600$.