Tag: calculations and mental strategies 1

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

Three times a number is equal to two times of the other. Find the ratio of 3 times the sum and 5 times the difference of the two numbers.

  1. 2

  2. 4

  3. 1

  4. 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the two numbers be x and y. We are given 3x = 2y, which implies x/y = 2/3, or let x = 2k and y = 3k. The sum of the numbers is 5k, so 3 times the sum is 3(5k) = 15k. The difference is y - x = k, so 5 times the difference is 5(1k) = 5k. The ratio of 3 times the sum to 5 times the difference is 15k / 5k = 3.

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

There are m men and two women participating in a chess tournament. Each participate plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84$, then the value of m is?

  1. $9$
  2. $7$
  3. $11$
  4. $12$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

x years ago, the difference between the ages of Hari and Sadu was y years. Then after z years what will be the difference between their ages?

  1. x years

  2. y years

  3. z years
  4. $(x+y+z)$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference between the ages of two people remains constant over time regardless of past or future years. Therefore, if the difference was y years x years ago, it will still be y years after z years.

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

The present age of Sohan is $20$ years more than the present age of Sachin. $3$ years hence, it will be thrice that of Sachin. Find the present age of Sohan.

  1. $23$ years
  2. $27$ years
  3. $30$ years
  4. $37$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Sachin's present age be S. Sohan's present age is S + 20. 3 years hence, Sohan's age will be S + 23 and Sachin's age will be S + 3. We are given S + 23 = 3(S + 3), which expands to S + 23 = 3S + 9, resulting in 2S = 14 and S = 7. Therefore, Sohan's present age is 7 + 20 = 27 years.

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

There are $2$ boxes A and B. If we take out $10$ apples from A box & put these apples in B box then the number of apples in B box will be $4$ times of A box. If we take out $5$ apples from B box & put these apples into A box then the number of apples in both A & B boxes will be same in numbers. Find out the total apples in both the boxes :

  1. $20$
  2. $30$
  3. $50$
  4. $60$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and B be initial apples. (A-10) = 4(B+10) is wrong; it should be (B+10) = 4(A-10). Also (A+5) = (B-5). From second: B = A + 10. Substitute into first: (A+10)+10 = 4(A-10) -> A+20 = 4A-40 -> 3A = 60 -> A = 20. Then B = 30. Total = 50.

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

In an examination, the ratio of passes to failures was 4 : 1. Had 30 less appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1. Find the number of students who appeared for the examination.

  1. $260$
  2. $112$
  3. $2166$
  4. $150$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$
Let\quad the\quad pass:\quad fail\quad =\quad 4:1\ If\quad fail\quad students\quad =x,\quad pass\quad students\quad =4x\ Total\quad students\quad =\quad 5x\ If\quad 30\quad less\quad appeared\quad and\quad 20\quad less\quad passed..\ Students\quad appearing\quad =\quad 5x\quad -30\ Students\quad passing\quad =\quad 4x\quad -\quad 20\ Students\quad failing\quad =\quad 5x\quad -\quad 30\quad -(4x\quad -20)\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\quad x\quad -10\ 4x\quad -20\quad :\quad x-10\quad ::\quad 5:1\ 4x\quad -20\quad =\quad 5(x-10)\ 4x\quad -\quad 20\quad =\quad 5x\quad -\quad 50\ x\quad =\quad 30\ Students\quad failing\quad =\quad 30\ Students\quad passing\quad \quad =\quad 4x\quad =120\ Totla\quad students\quad =\quad 5x\quad =\quad 150\ \ \ \ 
$

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

$A$ is older than $B$. Taking present ages of $A$ and $B$ as $x$ years and $y$ years respectively, find in terms of $x$ and $y$. The difference between the ages of A and B.

  1. $(2x - y) years$
  2. $(x - 3y) years$
  3. $(x - y) years$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given, 
$A$ is older than $B$. Taking present ages of $A$ and $B$ as $x$ years and $y$ years respectively.
The difference between the ages of A and B.

$ = (x - y) $

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

A boy was asked to multiply a certain number by $25$. He multiplied it by $52$ and got his answer more than the correct one by $324$. The number to be multiplied was:

  1. $12$
  2. $15$
  3. $25$
  4. $52$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Suppose  the number to be multiplied $= x$
As per Question
$\Rightarrow 52\times x = 25\times x + 324$
$ \Rightarrow 52x = 25x + 324$
$\Rightarrow  52x - 25x = 324$
$\Rightarrow 27x = 324$
$ x = 12 $
Hence, option 'A' is correct.

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

An old rhyme and problem:

If to my age, there added be,
One half of it and three times three,
Four score and seven my age will be,
How old am I, pray tell me?

  1. $52$ years
  2. $50$ years
  3. $48$ years
  4. $54$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$1$ score $= 20$ years

Let the age be $x$.
Then, $x + \dfrac{1}{2}x + 3\times 3 = 4 \times 20 + 7$
$\Rightarrow  \dfrac{3}{2}x + 9 = 80 + 7$
$\Rightarrow  \dfrac{3}{2}x = 78$
$\Rightarrow  x = 78 \times \dfrac{2}{3}$
$\Rightarrow  x = 52$
Therefore, the age is $52$ years.