Tag: maths

Questions Related to maths

The algebraic expression for the statement 'thrice of $x$ is added to $y$ multiplied by itself' is __________.

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

  1. $3x + 2y$

  2. $3x + y^{2}$

  3. $3(x + y^{2})$

  4. $3x + y$

Show answer
Correct Option: B
Explanation:

Thrice of $x$ $=$ $3x$


$y$ multiplied by itself $=$ $y\times y=y²$
 
According to question, we have

The algebraic expression is $3x+ y²$.

Aanya got $5$ marks in Science test. Her friend Sneha got $'x'$ marks more than Aanya. How many marks did they get altogether?

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

  1. $5\times x$

  2. $5 + x$

  3. $10 + x$

  4. $2x + 5$

Show answer
Correct Option: C
Explanation:

Marks obtained by Aanya $= 5$
Marks obtained by Sneha $= x + 5$
$\therefore$ Mark obtained by both of them
$= 5 + (x + 5) = x + 10$.

Match the following.

Column - I Column II
(i) The total mass of $3$ boxes is $5\ kg$. The mass of two of the boxes is $x\ kg$ each. The mass of third box is (a) $x - 11$
(ii) Sid had $x$ eggs. He used $5$ eggs to bake a cake and gave $6$ eggs to his neighbour. The number of eggs left with him is (b) $\dfrac {x}{3}$
(iii) Mohit had $Rs. x$. He gave the money to his $3$ sisters equally. Each girl get Rs. (c) $5 - 2x$
maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $(i)\rightarrow (c), (ii) \rightarrow (a), (iii) \rightarrow (b)$

  2. $(i)\rightarrow (b), (ii) \rightarrow (c), (iii) \rightarrow (a)$

  3. $(i)]\rightarrow (c), (ii) \rightarrow (b), (iii) \rightarrow (a)$

  4. $(i)\rightarrow (a), (ii) \rightarrow (b), (iii) \rightarrow (c)$

Show answer
Correct Option: A
Explanation:

(i) Given: Total mass of $3$ boxes is $5$ kg. 

Mass of each boxes out of two $=x$ kg each
$\therefore$ total mass of two boxes $=2x $ kg
Mass of $2$ boxes $+$ Mass of 3rd box $= 5$ kg
$\therefore$ Mass of 3rd Box $=5- 2x$ kg (c)

(ii) No of eggs Sid had $=x$ 
No of eggs used to bake a cake $= 5$
No of eggs given to neighbour $= 6$
$\therefore$ No of eggs left $= x-5-6= x-11$ (a)

(iii) Amount of money Mohit had $=Rs. x$
Amount of money divided equally among sisters = $Rs \dfrac{x}{3}$ (b)

Find the cost of $3$ notebooks and $1$ magazine in terms of y, if the cost of $1$ notebook is Rs.$2y$ and that of $1$ magazine is $Rs. (y+3)$.

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

  1. $Rs.(3y+3)$

  2. $Rs.(6y+3)$

  3. $Rs.(7y+3)$

  4. $Rs.(8y+3)$

Show answer
Correct Option: C
Explanation:
 The no. of notebooks is =3 then
total cost of notebooks is = $3\times 2y=6y$
cost of one magazine is =(y+3)
hence total cost =$6y+y+3=(7y+3)$
then optiuon $C$is correct. 

In the last three months Mr.Sharma lost $5\frac{1}{2}$kg, gained $2\frac{1}{4}$ kg and then lost $3\frac{3}{4}$ kg weight. If he now weighs $95$kg, then how much did Mr.Sharma weighs in beginning?

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

  1. $100$kg

  2. $102$kg

  3. $106.5$kg

  4. $104$kg

Show answer
Correct Option: B
Explanation:

Let $x$ be the weight of Mr. Sharma in beginning.


According to given details,
$x-5.5+2.25-3.75=95$
$\Rightarrow x=95+5.5+3.75-2.25=95+7=102\ kg$.

So, the answer is $102\ kg$.  $[B]$

In an alloy of zinc, tin and lead, quantity of zinc is $\left(\cfrac{3}{4}\right)^{th}$ that of tin and quantity of tin is $\left(\cfrac{4}{5}\right)^{th}$ that of lead. How much of each metal will be there in $12$ kg of the alloy?

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

  1. $5,4,3$

  2. $3,4,5$

  3. $4,5,3$

  4. $5,3,4$

Show answer
Correct Option: D
Explanation:

  • Let the quantity of the tin be $'x'$ , zinc be $'y'$ and lead be $'z'$.
Given quantity of zinc is $\cfrac{3}{4}th$ of tin,
$\implies y=\cfrac{3}{4}(x)--------(1)$
Quantity of tin is $\cfrac{4}{5}th $ of lead,
$\implies x=\cfrac{4}{5}(z)------(2)$
But given total weight $=12kg$
$\implies x+y+z=12$
From $(1)&(2) $equations
$x+\cfrac{3}{4}x+\cfrac{5x}{4}=12$
$\cfrac{12x}{4}=12$
$\implies x=4$
if $x=4, y=3,z=5$
So the quantity of tin is $4kg$ , zinc is $3kg$ , lead is $5kg$

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. $5$

Show answer
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. $-1$

Show answer
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 $

Show answer
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, $10.5x=14$

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

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

$\therefore c=6$.