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

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

  1. $12$
  2. $15$
  3. $16$
  4. $19$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $16$.
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

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: 

  1. $55$
  2. $60$
  3. $62.5$
  4. $64$
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

$\Rightarrow 180+3x=360$

$\Rightarrow 3x=360-180$

$\Rightarrow 3x=180$

$\Rightarrow x=60$.
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

$8$% 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?

  1. $21000$
  2. $23500$
  3. $22000$
  4. $27500$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let T be the total voters. 92 percent of T cast votes. Winner got 48 percent of T, so loser got (92-48)=44 percent of T. The difference is 4 percent of T = 1100. T = 1100/0.04 = 27500.

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

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

  1. $l \times l \times l$
  2. $3 \times 3 \times 3$
  3. $3 \times l$
  4. $3 + l$
Reveal answer Fill a bubble to check yourself
C Correct answer
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$3\times side=3\times l$
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

If a $\in { 1,2,3,4 } ,$ then number of equations of the form $x ^ { 2 } + a x + 1 = 0$ having real roots is

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For real roots, the discriminant D = a^2 - 4 >= 0. This implies a^2 >= 4. Given a in {1, 2, 3, 4}, the values satisfying this are a=2, 3, 4. There are 3 such values.

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

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digit of that number ?

  1. 3

  2. 4

  3. 9

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let the ten's digit be $x$ and unit's digit be $y$.

Then, $(10x + y) - (10y + x) = 36$

$9(x - y) = 36$

$x - y = 4$

Therefore, the difference between the two digit of that number is $4$