Tag: calculations and mental strategies 1

Questions Related to calculations and mental strategies 1

Four years ago, the father's age was three times the age of his son. The total of the age of the father and the son after four years will be $64$ years. What is the father's age at present?

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

  1. $32$ years

  2. $36$ years

  3. $44$ years

  4. $40$ years

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Correct Option: D
Explanation:

fathers present age $= x$ years.

sons present age $= y$ years.  

four years ago, fathers age $=3 \times $ sons age.
$(x-4)=(y-4)\times 3$
$x=3y-8$.....(i) 

after 4 years, fathers age$ +$ sons age $= 64 $
$x+4+y+4=64 $
$x+y=56$.....(ii) 

solve for $x$
$x=3\times 56-3x-8$ 
$4x=160$ 
$x=40$ years  

D is correct.   

The area of a field in the shape of a trapezium measures $1440{m}^{2}$. The perpendicular distance between its parallel sides is $24m$. If the ratio of the parallel sides is $5:3$, the length of the longer parallel side is:

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

  1. $45m$

  2. $60m$

  3. $75m$

  4. $120m$

Show answer
Correct Option: C
Explanation:
Parallel sides $= 5x,\, 3x$
area $=\dfrac{24}{2}(5x+3x)=1440 $
$12(8x)=1440$
$x=\dfrac{120}{8}=15$ 
$5x=15\times 5$ 
     $=75m$

If $\left(\dfrac { 3 } { 4 }\right)^{th}$ of $x$ of $\left(\dfrac { 1 } { 4 }\right)^{th}$ of $35600 = 1668.75 ,$ find $x$

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

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

  2. $\dfrac { 3 } { 4 }$

  3. $\dfrac { 2 } { 5 }$

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

Show answer
Correct Option: D
Explanation:

$\dfrac { 3 }{ 4 } \times x\times \dfrac { 1 }{ 4 } \times 35600=1668.75$

$\Rightarrow x=\dfrac { 1668.75\times 16 }{ 3\times 35600 } =\dfrac { 1 }{ 4 } $      [D]

If a function $f$ is linear with $f(0)=5$ and $f(2)=9$ then find $f(9)$

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

  1. 23

  2. 25

  3. 26

  4. none of these

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Correct Option: A
Explanation:

$f$ is a linear function 

So Let $f=ax+b$
$f(0)=a(0)+b=5\\implies b=5\cdots(1)\f(2)=9\a(2)+5=9\\implies a=2\f(x)=2x+5\f(9)=2(9)+5\18+5=23$

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

Show answer
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

Show answer
Correct Option: A
Explanation:

Let $l$ be the length of a room 

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