Tag: calculating and mental strategies 3

Questions Related to calculating and mental strategies 3

Two numbers are less than a third number by $30\%$ and $37\%$ respectively. How much percent is the second number less than the first?

maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

  1. $10\%$

  2. $15\%$

  3. $20\%$

  4. $25\%$

Show answer
Correct Option: A
Explanation:

Let the $3rd$ number be $100$. Then,


$1st$ number $= 70$ and $2nd$ number $= 63$

$2nd$ number is less than 1st by $(\dfrac{7}{70}\times 100)=10 \%$

Choose the correct answer from the alternative given. 
A man had $100$ kgs of sugar, part of which he sold at $7\%$ profit and rest at $17\%$ profit. He gained $10\%$ on the whole. How much did he sell at $7\%$ profit?

maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

  1. $65$kg

  2. $35$kg

  3. $30$kg

  4. $70$kg

Show answer
Correct Option: D

$83.33\% $ of coins out of $36$ coins are $20$ paise coins and rest are $10$ paise coins which amounts to $6.60$. Find the number of $10$ paise coins.

maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

  1. $8$

  2. $5$

  3. $6$

  4. $2$

Show answer
Correct Option: C
Explanation:

Given : $83.33$% of $36$ coins are $20$ paisa coins

$83.33$% of $36 =\left( \cfrac { 83.33 }{ 100 }  \right) \times 36=30$

So, $30$ coins are $20$ paise coins and remaining $(36-30)= 6$ coins are $10$ paise coins.

Value $=30\times 20+6\times 10=660$ Paise $=Rs. 6.60$, which is the given amount.

$\therefore $ Number of $10$ paise coins are $6$.

Choose the correct answer from the alternatives given.
The average age of eleven cricket players is 20 years. If the age of the coach is also included, the average age increases by 10%. The age of the coach is

maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

  1. 48 year

  2. 44 year

  3. 40 year

  4. 36 year

Show answer
Correct Option: B
Explanation:

Average of 11 players $= 20$ years.
Sum of age of 11 players $= 20 \times 11 = 220$
Average age of players and coach $1.1 \times 20 22$ years
Sum of ages of players & coach $= 22 \times 12 = 264$ years.
Age of coach $= 264 - 220 = 44$ years. 

Express as rupees using decimals,

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $5\ paise$

  2. $75\ paise$

  3. $20\ paise$

  4. $50\ rupees\ 90\ paise$

Show answer
Correct Option: A
Explanation:
let $1paisa$ =$100 rs$
So,
$(i).$
$=>5paisa=\dfrac{5}{100}=0.005rs$

$(ii).$

$=>75paisa=\dfrac{75}{100}=\dfrac{3}{4}=0.75rs$

$(iii).$
$20paisa=\dfrac{20}{100}=0.2rs$

$(iv).$

$50rs$ $90paisa=50rs+90paisa$

$=>50+\dfrac{90}{100}$

$>=50+0.9=50.9rs$


























Find the value of $x$: $10.5 \div x = 1.05 \div 0.5$.

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $0.05$

  2. $105$

  3. $0.105$

  4. $5$

Show answer
Correct Option: D
Explanation:

$\displaystyle\frac { 10.5 }{ x } = \displaystyle\frac { 1.05 }{ 0.5 } $

$x = \displaystyle\frac { 10.5\times 0.5 }{ 1.05 } = \displaystyle\frac { 105\times 5 }{ 105 } = 5$

If $\displaystyle\frac { 1 }{ 6.198 } = 0.16134$, then the value of $\displaystyle\frac { 1 }{ 0.0006198 } $ is.

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $16134$

  2. $1613.4$

  3. $0.16134$

  4. $0.016134$

Show answer
Correct Option: B
Explanation:

$\displaystyle\frac { 1 }{ 0.0006198 } = \displaystyle\frac { 1 }{ \displaystyle\frac { 6.198 }{ 10000 }  } = \displaystyle\frac { 10000 }{ 6.198 } $

$= 10000 \times 0.16134 = 1613.4$

Consider the following quotients:
I.   $368.39$ divided by $17$.
II.  $170.50$ divided by $62$.
III. $875.65$ divided by $83$.
Their correct sequence in decreasing order is ?

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. I, III, II

  2. II, I, III

  3. II, III, I

  4. III, I, II

Show answer
Correct Option: A
Explanation:

(I) $\displaystyle\frac{368.39}{17} = 21.67$


(II) $\displaystyle\frac{170.50}{62} = 2.75$
(III) $\displaystyle\frac{875.65}{83} = 10.55$
$\therefore$ The correct sequence in decreasing order is (I), (III), (II).

Simplified value for $(17.5+2.5)\div 5$ is

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: D
Explanation:

$\left( 17.5+2.5 \right) \div 5$

$=\left( 20.0 \right) \div 5$
$ =20\div 5$

$ =4$
So, correct answer is option D.

If $\displaystyle \frac{547.527}{0.0082}=x $, then the value of $\displaystyle \frac{547527}{82}$ is 

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $\displaystyle \frac{x}{10}$

  2. 10x

  3. 100x

  4. $\displaystyle \frac{x}{100}$

Show answer
Correct Option: A
Explanation:

Given, $\displaystyle \frac{547.527}{0.0082}=x $


$\displaystyle \Rightarrow \frac{5475270}{82}=x $

$\displaystyle \Rightarrow \frac{5475270}{82}=\frac{x}{10} $