Tag: maths

Questions Related to maths

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

introduction to ratio and percentages comparing quantities maths

  1. $66\dfrac {2}{3}$

  2. $100$

  3. $105\dfrac {1}{3}$

  4. $120$

Show answer
Correct Option: B
Explanation:

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

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?

introduction to ratio and percentages comparing quantities maths

  1. $10$ min. $20$sec.

  2. $11$ min. $45$sec.

  3. $12$ min. $30$ sec.

  4. $14$ min. $40$ sec.

Show answer
Correct Option: D
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.

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.

introduction to ratio and percentages comparing quantities maths

  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.

Show answer
Correct Option: C
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.

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

introduction to ratio and percentages comparing quantities maths

  1. $43.75\%$

  2. $21.88\%$

  3. $50\%$

  4. $25\%$

Show answer
Correct Option: A
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=$\displaystyle\frac{\displaystyle\frac{9}{16}\pi d^2-\pi d^2}{\pi d^2}\times 100=-43.75\%$

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

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

  1. $38,68,60,000$

  2. $38,65,600$

  3. $38,65,00,000$

  4. $38,66,00,000$

Show answer
Correct Option: D
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 $38,66,00,000$

Round off  $231$ to nearest $100.$

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

  1. $200$

  2. $300$

  3. $250$

  4. $350$

Show answer
Correct Option: A
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 $200$.

Round off $829$ to nearest $100$. 

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

  1. $800$

  2. $700$

  3. $900$

  4. $850$

Show answer
Correct Option: A
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 $800$.

Round off $7065$ to nearest $1000$  :

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

  1. $700$

  2. $7000$

  3. $70$

  4. $7$

Show answer
Correct Option: B
Explanation:

Rounding off $7065$ to nearest $1000$ we check if $065$ is less than $500$ or not,

As $065 < 500$, we round it off to $000$

$\therefore 7065$ to nearest $1000$ equals $7000$

Round off  $63$ to nearest $10$ 

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

  1. $60$

  2. $70$

  3. $65$

  4. $63$

Show answer
Correct Option: A
Explanation:

Rounding off $63$ to nearest $10$ we check if $3$ is less than $5$ or not,

As $3 < 5$, we round it off to $0$

$\therefore 63$ to nearest $10$ equals $60$

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

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

  1. $1630,1600$

  2. $1640,1730$

  3. $1740,1700$

  4. $1640,1734$

Show answer
Correct Option: A
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 $1600$.