Tag: calculations

Questions Related to calculations

The ratio at which the point $(5,4)$ divides the line $(3,2)$ and $(8,7)$

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $\dfrac 23$

  2. $\dfrac{-3}{2}$

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

  4. $\dfrac{1}{9}$

Show answer
Correct Option: A
Explanation:
Given points $(3,2);(8,7)$
Let the ratio be $m:n$
The dividing point is given as $\dfrac{8m+3n}{m+n}=5\\8m+3n=5m+5n\\3m=2n\\\dfrac mn=\dfrac 23$

Mr Sahoo attended a 1-day workshop from 09:15 a.m. to half five in the evening. The workshop included a $1\frac{1}{4}$ hour lunch break, two 15 minutes tea breaks and 13 activities, each of equal duration. Calculate the duration of each activity.

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $30$ minutes

  2. $20$ minutes

  3. $25$ minutes

  4. $40$ minutes

Show answer
Correct Option: A
Explanation:

Total time of the workshop =$8$ hours and $15$ min

$=8 \times 60+15=495 $ min

Total time of tea break = $30$ min

lunch break time = $75$ min

hence time available for 13 activities 
$=495-75-30$ $=6$ hours and $30$ min
$=390 $ min

So, time devoted to each activity $=\dfrac{390}{13}=30$ min

The greatest length which may be used to measure exactly $\displaystyle13\frac{3}{4}:ft$., $\displaystyle17\frac{1}{2}$., 20 ft. and $\displaystyle21\frac{1}{4}:ft$. is given by

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. 3"

  2. 15"

  3. 18"

  4. 21"

Show answer
Correct Option: B
Explanation:

$\displaystyle13\frac{3}{4}:ft=165:inches$

$\displaystyle17\frac{1}{2}:ft=210:inches$ 

$20:ft=240:inches$ 

and $\displaystyle21\frac{1}{4}:ft=255:inches$ 

In order to find the greatest length we have to find the G. C. M. of 165", 210", 240" and 255" and the G. C. M. of these four numbers is 15".

One inch is equivalent to $2.54$ cm. How many centimeters are in two feet? Round your answer to two decimal places.

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $5.08$ cm

  2. $12.62$ cm

  3. $60.96$ cm

  4. $30.48$ cm

Show answer
Correct Option: C
Explanation:

First convert 2 feet to inches and then convert the result to centimeters. One foot is equivalent to 12 inches, so there are 24 inches in 2 feet. Since there are 2.54 cm in a foot, multiply 24 by 2.54 to convert feet to centimeters.
$24$ $\times$ $2.54 = 60.96$
Therefore, there are $60.96$ cm in $2$ feet.

Subtract $778\ m\ 78\ cm$ from $2\ km\ 768\ cm$

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $1228.9\ m$

  2. $571.1\ m$

  3. $1221.988\ m$

  4. $189.22\ m$

Show answer
Correct Option: A
Explanation:

First we have to convert both the quantities in $m$

$1\ \ m=100\ \ cm$
$\Rightarrow 1\ \ cm=.01 \ m$
$778 \ \ m\ \ 78\ \ cm =778+.01\times 78=778.78\ \ m$
$1\ \ km=1000\ \ m$
$2\ \ km\ \ 768\ \ cm =2\times1000+.01\times768=2007.68\ \ m$
Now subtracting both 
$2007.86-778.8=1128.9\ \ m$
Option $A$ is correct.

Add $1.25\ cm$ and $13.45\ cm$

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $2.595$

  2. $1.470$

  3. $14.70$

  4. $25.95$

Show answer
Correct Option: C
Explanation:

$1.25\ \ cm+13.45\ \ cm=14.70\ \ cm$

So option $C$ is correct.

Subtract :
$23.67\ m$ from $1.4\ km$

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $116.33$

  2. $1376.33\ m$

  3. $13976.33\ m$

  4. $22.27\ m$

Show answer
Correct Option: B
Explanation:

First we have to convert $km$ into $m$

$1\ \ km=1000\ \ m$
$\Rightarrow 1.4\ \ km=1.4\times1000=1400\ \ m$
Now subtracting both
$1400 \ \ m-23.67\ \ m=1376.33\ \ m$
So option $C$ is correct.

Add $23.456\ m$ and $26.5\ cm$ .

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $499.56\ cm$

  2. $49.956\ cm$

  3. $237.16\ cm$

  4. $2372.6\ cm$

Show answer
Correct Option: D
Explanation:
First we have to convert $m$ into $cm$
$1\ \ m=100\ \ cm$
$\Rightarrow 23.456\ \ m=23.456\times100=2345.6\ \ cm$
Now adding both
$2345.6\ \ cm+26.5\ \ cm=2372.6\ \ cm$
None of the options are correct

A pole is painted yellow and black. The yellow part is $1.8\ m$ long and the black is three times longer than yellow part. Find the length of pole.

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $5.4\ m$

  2. $7.2\ m$

  3. $3.6\ m$

  4. $none\ of\ these$

Show answer
Correct Option: B
Explanation:

Length of yellow Part $=Y=1.8m$

Length of Black Part $=3Y=5.4m=B$
So, Length of Pole $=L=Y+B=1.8+5.4=7.2m$

Rita had $\displaystyle 38\frac { 1 }{ 4 } $ m long rope. She cut it into 5 equal parts. Then the length of each piece will be- 

maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

  1. $\displaystyle 1\frac { 1 }{ 4 } $ m

  2. $\displaystyle 2\frac { 3 }{ 4 } $ m

  3. $\displaystyle 3\frac { 1 }{ 4 } $ m

  4. $\displaystyle 1\frac { 3 }{ 4 } $ m

Show answer
Correct Option: D
Explanation:

Length of the rope $\displaystyle= 8\dfrac { 3 }{ 4 } m\ Number\quad of\quad peices\quad cut\quad =5\ Length\quad of\quad each\quad peice\quad =8\dfrac { 3 }{ 4 } m\div 5=\dfrac { 35 }{ 4 } m\times \dfrac { 1 }{ 5 } \ =\left( \dfrac { 35 }{ 4 } \times \dfrac { 1 }{ 5 }  \right) m=\dfrac { 7 }{ 4 } m=1\dfrac { 3 }{ 4 } m\ \therefore The\quad length\quad of\quad each\quad piece\quad of\quad the\quad rope\quad =1\dfrac { 3 }{ 4 } m.$