Tag: basic operations with same units

Questions Related to basic operations with same units

A shopkeeper purchased $346$ kg $500$ g of orange. Later on, he found that $109$ kg $300$ g of oranges were rotten. Find the quantity of oranges in good condition.

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $150$ kg $670$ g

  2. $204$ kg $600$ g

  3. $237$ kg $200$ g

  4. $250$ kg $940$ g

Show answer
Correct Option: C
Explanation:

We know that $gram$  is abbreviated as $gm$

$1$  $kg =1000$  $gram$
Total  weight of  Oranges purchased $ = B = $   $346$ $kg$  $500$  $gm$ 
Total weight of rotten oranges $=A = $   $109$ $kg$  $300$  $gm$ 
(i) We have to subtract $109\ kg$ $300\ gm$ from $346$ $kg$  $500$  $gm$ to get the weight of good conditioned oranges

$109$ $kg$  $300$  $gm$ $ = 109kg + 300gm$  $=A $   ...................(1)

$346$ $kg$  $500$  $gm$ $ = 346kg + 500gm$  $=B $   ...................(2)


$B-A = [346\ kg+500\ gm]-[109\ kg +300\ gm]$
$ = [346\ kg-109\ kg] +  $ $[500$ $gm$ $-$ $300$  $gm$]
$= 237  $  $kg $ $+  $  $200$ $gm$ 

Therefore, $237  $  $kg $  $200$ $gm$   of oranges are in good condition.

How much heavier is the toffee packet which has mass $1$ kg $345$ g in comparison to $1$ kg of chocolates?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $1$ kg $345$ g

  2. $345$ g

  3. $1$ kg

  4. $1$ kg $234$ g

Show answer
Correct Option: B
Explanation:

Weight of first toffee packet $=1.345\ kg$ 


Weight of second toffee packet $=1\ kg$ 

Required difference
$=1.345-1$

$=0.345\ kg$

$=345\ gm$

Hence, this is the answer.

If $15$ bananas measure $1.2$ kg, then find the weight of one banana. (Give yous answer in grams)

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $80$ gms

  2. $70$ gms

  3. $60$ gms

  4. $50$ gms

Show answer
Correct Option: A
Explanation:

Total number of Bananas $=15$


Total mass of 15 Bananas  $=1.2 kg$

Total mass of $1$ banana $=\dfrac{1.2}{15} $   $kg$

We know that

$1$  $kg =1000$  $gram$

$1$  $gm =\dfrac1{1000}$  $kg$

we have to convert $\dfrac{1.2}{15}$  $kg$  to   $grams$


$\dfrac{1.2}{15}$  $kg =\dfrac{1.2}{15} \times 1000$  $gm$

                $=80$  $gm$

So, Option $A $ is correct 

A hollow iron pipe is $21\,cm$ long and its external diameter is $8\,cm$. If the thickness of the pipe is $1\,cm$ and iron weighs $8\,g/c{m^3}$, then the weight of pipe is :

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $3.6\,kg$

  2. $3.696\,kg$

  3. $36\,kg$

  4. $36.9\,kg$

Show answer
Correct Option: B
Explanation:

Volume of iron $=\pi(R^2-r^2)\times h$


$=\pi(4^2-3^2)\times 21$

$=\cfrac{22}{7}\times(16-9)\times 21$

$=462cm^2$

Weight $=\cfrac{8\times 462}{1000}kg=3.696kg$

Working together, pipes $A$ and $B$ can fill an empty tank in $10\ hours$. they worked together for $4$ hours and then $B$ stopped and $A$ continued filling the tank till was full. It took a total of $13\ hours$ to fill the tank. How long would it take $A$  to fill the empty tank alone?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $13\ hours$

  2. $15\ hours$

  3. $17\ hours$

  4. $18\ hours$

Show answer
Correct Option: B

A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all  round. Find the weight, in the kilogram, of 2 meters of the pipe if 1 $\displaystyle cm^{3}$ of the metal weighs 7.7 g.

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. 12.31 kg

  2. 19.31 kg

  3. 13.31 kg

  4. 14.31 kg

Show answer
Correct Option: C
Explanation:

Inner diameter=5 cm. radius=2.5cm
thickness =5mm=0.5cm
outer radius=2.5+0.5=3cm
length=2m=200cm
volume of pipe=
$V=\Pi { (R }^{ 2 }-{ r }^{ 2 })h$
$V=3.14{ (3 }^{ 2 }-{ 2.5 }^{ 2 })200$
$V=22/7(9-6.25)200$
$V=12100/7{ cm }^{ 3 }$
 1 $cm^3$ of the metal weighs 7.7 $g$.
$ So, \cfrac{12100}{7} cm^{3} \hspace {1 mm} weighs =7.7\cfrac{12100}{7} gm =13310 \hspace {1 mm} gm = 13.31 kg$
 

The average weight of three boys $P$, $Q$ and $R$ is $\displaystyle 54\frac {1}{3}$ $Kg$, while the average weight of three boys $Q$, $S$ and $T$ is $53$ $kg$. What is the average weight of $P$, $Q$, $R$, $S$ and $T$?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $52.4$ $kg$

  2. $53.2$ $kg$

  3. $53.8$ $kg$

  4. Data inadequate

Show answer
Correct Option: D
Explanation:

As per question, 
$P+Q+R=54\frac { 1 }{ 3 } $---------eq 1
$Q+S+T=53 $-----------eq2
Here is 5 variable and 2 euqation.Data inadequate to solve the question.
Answer (D) Data inadequate

How many smaller solid balls of radius 2 cm can be made by melting a solid sphere of radius 8 cm?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. 128

  2. 512

  3. 64

  4. 32

Show answer
Correct Option: C
Explanation:

Number of balls made $ = \dfrac {Volume  of   sphere } {Volume  of 

each  spherical  ball} $
Volume of a sphere of radius 'r' $ = \dfrac { 4 }{ 3 } \pi { r }^{ 3 } $

Hence, number of balls made $ =\dfrac { \dfrac { 4 }{ 3 } \pi \times  { 8 }^{ 3 } }{ \dfrac { 4 }{ 3 } \pi \times { 2 }^{ 3 } } = 64  $

If $\square =2$ and $\triangle =4$. Then $6\times \square - 3\times \triangle =$ ?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $0$

  2. $1$

  3. $3$

  4. $2$

Show answer
Correct Option: A
Explanation:
$\Box =2,\triangle =4,$, then $6\times \Box -3\times \triangle =?$
$\Rightarrow 6\times 2-3\times 4=12-12=0$

Weight of one balloon is $3$ gms and of one string is $4$ gms. Then what is the combined weight of $3$ balloons and $6$ strings ?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $9$ gms

  2. $24$ gms

  3. $33$ gms

  4. $41$ gms

Show answer
Correct Option: C
Explanation:

Total weight$=\left( 3\times 3 \right) +\left( 6\times 4 \right) =33 gm$