Tag: calculations and mental strategies 1

Questions Related to calculations and mental strategies 1

For a journey the cost of a child ticket is $\cfrac { 1 }{ 3 } $ of the cost of an adult ticket. If the cost of tickets for $4$ adults and $5$ children is Rs. $85$, the cost of a child ticket is

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

  1. Rs. $15$

  2. Rs. $6$

  3. Rs. $10$

  4. Rs. $5$

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Correct Option: A
Explanation:

Let the cost of an adult ticket be $y$ $\Rightarrow$ Child's ticket costs $\cfrac{1}{3}y$
$\Rightarrow 4y+\cfrac { 5 }{ 3 } y=85\Rightarrow 17y=225\Rightarrow y=Rs. 15\quad $
$\therefore$ cost of child's ticket $=Rs.15$

If  $2x  + 2(4 + 3x) < 2 + 3x > 2x + \dfrac{x}{2}$ then $x$ can take which of the following values. 

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

  1. $-3$

  2. $1$

  3. $0$

  4. $-1$

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Correct Option: A
Explanation:

Given,
$2x+2(4+3x) < 2+3x > 2x+\dfrac{x}{2}$

Solving $1^{st}$ inequality

$2x+8+6x < 2+3x$

$5x < -6$

$x < \dfrac{-6}{5}$

Solving $2^{nd}$ inequality

$2+3x > 2x+\dfrac{x}{2}$

$\dfrac{x}{2} > -2$

$x > -4$

$x\in \left (-4, \dfrac{-6}5\right )$

$x$ can take values $-3$

$A$ is correct.

Divide $Rs\ 1,545$ between three people $A,B$ and $C$ such that $A$ gets three-fifths of what $B$ gets and the ratio of the share of $B$ to $C$ is $6:11$.
what amount will each person get ?

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

  1. $A=240, \ B= 440, \ C=825$

  2. $A=230, \ B= 440, \ C=825$

  3. $A=270, \ B= 450, \ C=825$

  4. $A=245, \ B= 440, \ C=825$

Show answer
Correct Option: C
Explanation:
$3\times \dfrac {6x}{5}+6x+11x=1545$
$\dfrac {18x+30x+55x}{5}=1545$
$\dfrac {103x}{5}=1545$
$x=\dfrac {5\times 1545}{103}$
$x=75$
$A=\dfrac {18}{5}\times 75 =270$
$B=6\times 75 =450$
$C=11\times 75=825$


If $(a+b):(b+c):(c+a)=6:7:8$ and $(a+b+c)=14$ , then the value of $c$ is

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

  1. $6$

  2. $7$

  3. $8$

  4. $14 $

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Correct Option: A
Explanation:
$a+b:b+c:c+a=6:7:8$

$a+b+c=14$

$\therefore \dfrac{a+b}{b+c}=\dfrac{6}{7}$ ……..$(1)$

$\therefore \dfrac{b+c}{c+a}=\dfrac{7}{8}$ ……..$(2)$

$\therefore \dfrac{a+b}{c+a}=\dfrac{6}{8}$ ...........$(3)$

From $(1)$ & $(2)$

$\left.\begin{matrix}If & a+b=6x\\ then & b+c=7x\end{matrix}\right\}\rightarrow x\in R$

then $c+a=8x$

$\therefore 2(a+b+c)=6x+7x+8x$

$\therefore a+b+c=\dfrac{21x}{2}$

$\therefore a+b+c=10.5x$

$\therefore c=10.5x-6x$

$\therefore c=4.5x$

Also, $10.5x=14$

$\therefore x=\dfrac{14}{10.5}$

$\therefore c=\dfrac{4.5\times 14}{10.5}$

$\therefore c=6$.

In a two digit no. the digit at units place is $\left| x-2 \right| $ and digit at tens place is $\left| x+1 \right| $, then that number is

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

  1. 2x+3

  2. 11x+12

  3. 10x+1

  4. 11x+21

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Correct Option: A

if $76$ is divided into four parts proportional to $7,5,3.4$ then the smallest part is:

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

  1. $12$

  2. $15$

  3. $16$

  4. $19$

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Correct Option: A
Explanation:
Four parts proportional to 

$7,5,3$ and $4$

$\therefore $  Four part are equal to$7x, 5x, 3x,$ and $4x.$

$\therefore7x+5x+3x+4x=76$

$\therefore 19x=76$

$\therefore x=\dfrac {76}{19}$

$\therefore x=4$

$\therefore 7x=4\times7=28$

$\therefore 5x=5\times4=20$

$\therefore 3x=3\times 4=12$

$\therefore 4x=4\times4=16$

$\therefore $ For parts are $28, 20, 12$ and $16$.

The ratio of the volumes of water and glycerine in 240cc of mixture is 1:3 .The quantity of water (in cc) that should be added to the mixture so the volumes of water and glycerine 2:3 is: 

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

  1. $55$

  2. $60$

  3. $62.5$

  4. $64$

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Correct Option: B
Explanation:
The ratio of the volume of water and Glycerine in $240$cc of mixture is $1:3$. 

The quantity of water(in cc) that should be added to the mixture so that the new ratio of the volume of water and glycerine becomes $2:3$

Let the ratio of the volume of water and glycerine be $x$ and $3x$.

$x+3x=240$

$\Rightarrow 4x=240$

$\Rightarrow x=60$

So the volume of water is $60cc$

Volume of glycerine is $60cc$

Volume of glycerine is $(3\times 60)cc=180$cc

Let x litre of water is added

$\dfrac{60+x}{180}=\dfrac{2}{3}$

$\Rightarrow 3(60+x)=360$

$\Rightarrow 180+3x=360$

$\Rightarrow 3x=360-180$

$\Rightarrow 3x=180$

$\Rightarrow x=60$.

$8$% of the voters in an election did not cast their votes. In this election, there were only two candidates. The winner by obtaining $48$% of the total votes, defeated his contestant by $1100$ votes. The total number of voters in the election was?

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

  1. $21000$

  2. $23500$

  3. $22000$

  4. $27500$

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Correct Option: D

Which of the equation satisfy the given statement ?
"Perimeter of an equilateral triangle is three times its side l" 

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

  1. $l \times l \times l$

  2. $3 \times 3 \times 3$

  3. $3 \times l$

  4. $3 + l$

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Correct Option: C
Explanation:
An equilateral triangle is a triangle in which all three sides are equal.Let $l$ be the length of the side of a triangle.
Thus, perimeter is equal to sum of all its sides$3\times side=3\times l$

Equation of the statement 'Thrice the length (l) of room is $340$ metres' is ____ 

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

  1. $3l=430$

  2. $3l=340$

  3. $3+l=340$

  4. $3l+340=0$

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Correct Option: B
Explanation:

Let $l$ be the length of the room

Thrice the length of the room$=3l$
Given:Thrice the length of the room$=340\ m$
Equation is $3l=340\ m$