Tag: maths

Questions Related to maths

If $(30 + x) : (23 + x) = 5 : 4$ then find the value of x.

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 5

  2. 6

  3. 4

  4. 7

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Correct Option: A
Explanation:

$ => 30 + x : 23 + x = 5:4 $


$ => \frac {30 + x}{23 + x} = \frac {5}{4} $

Cross multiplying, 

$ 120 + 4x = 115 + 5x $


$ 120 - 115 = 5x - 4x $


$ x = 5 $

Translate the following sentence into an algebraic equation: "13 diminished from twice a number is equal to 17"

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $2x-13=17$

  2. $13-2x=17$

  3. $2x-17=13$

  4. $2x+13=17$

Show answer
Correct Option: A
Explanation:

Let  the  number  be  $x.$


Twice  of  the  number  is  $2x$  and  $13$  is  diminished  from  $2x$  means  $(2x-13)$  and  it  is  equal   to   $17. $
 So  answer  is  option  A

'8 is less than twenty times a' is written as 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 8 - 20a

  2. 20ac

  3. 8 < 20 $\times$ a - 8

  4. 20a - 8

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Correct Option: D
Explanation:

Eq : 20a - 8

Algebraic expression for the statement 8 times a taken away from 60 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 8a - 60

  2. 60 - 8a

  3. 0

  4. 60a - 8

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Correct Option: B
Explanation:

Eq : 20a - 8

The equation for the statement : 'half of a number added to 20 is 25' 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $\displaystyle{\frac{x}{4}}$ + 20 = 25

  2. $\displaystyle{\frac{x}{5}}$ + 25 = 20

  3. $\displaystyle{\frac{x}{2}}$ + 20 = 25

  4. $\displaystyle{\frac{x}{3}}$ + 20 = 25

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Correct Option: C
Explanation:

$\displaystyle{\frac{x}{2}}$ + 20 = 25 

Half of the number added to 20 will give the answer 25
$\dfrac{10}{2} +20=25$

Equation of the statement : 'Thrice the length of a room is $240$ metres.' 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $3l = 240$

  2. $3 + l = 40$

  3. $3l = 420$

  4. None of these

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Correct Option: A
Explanation:

Let $l$ be the length of a room 

therefore according to statement, required equation is   
$3l = 240 $

Equation for the statement: 'thrice the length (L) of a room is 340 metres'

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $3L = 43$

  2. $3L = 340$

  3. $3 + L= 34$

  4. None of these

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Correct Option: B
Explanation:

$\Rightarrow$  The length of room is $L.$

$\Rightarrow$  So, thrice the length means $3L.$

The equation for thrice the length of the room is $340 \ meters$

$\Rightarrow$  $3L=340\ meters.$

The equation for the statement:"half a number added to 10 is 15".

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $\dfrac{X}{2}\,+ 10\,+ 5$

  2. $\dfrac{X}{2}\,+ 10\,= 5$

  3. $\dfrac{X}{2}\,+ 15\,= 10$

  4. $\dfrac{X}{2}\,= -10\,+ 15$

Show answer
Correct Option: D
Explanation:

Let the number be $X.$

Half of the number is $\dfrac{X}{2}$
Half a number added to $10$ is $\dfrac{X}{2}+10$
So, according to the question,
$\Rightarrow$  $\dfrac{X}{2}+10=15$

$\Rightarrow$  $\dfrac{X}{2}=-10+15$

In three coloured boxes - Red, Green and Blue, $108$ balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $18$

  2. $36$

  3. $45$

  4. None of these

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Correct Option: D

The following expressions in statement is given as:
$x+3$

3 is added to x

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. True

  2. False

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Correct Option: A
Explanation:

Yes the  statement is correct. This defines the expression in words.