Tag: equations from statements

Questions Related to equations from 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.

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

  1. 2

  2. 4

  3. 1

  4. 3

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Correct Option: A

In a two-digit number, the tens digit is one more than twice the units digit. The sum of the digits is $36$ less than the number formed by reversing the digits. Find the product of the digits.

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

  1. $56$

  2. $12$

  3. $24$

  4. $36$

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Correct Option: A

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?

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

  1. $9$

  2. $7$

  3. $11$

  4. $12$

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Correct Option: A

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?

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

  1. x years

  2. y years

  3. z years

  4. $(x+y+z)$ years

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Correct Option: A

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.

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

  1. $23$ years

  2. $27$ years

  3. $30$ years

  4. $37$ years

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Correct Option: A

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 :

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

  1. $20$

  2. $30$

  3. $50$

  4. $60$

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Correct Option: C

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.

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

  1. $260$

  2. $112$

  3. $2166$

  4. $150$

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Correct Option: D
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\ \ \ \ 
$

$A$ 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.

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

  1. $(2x - y) years$

  2. $(x - 3y) years$

  3. $(x - y) years$

  4. None of these

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Correct Option: C
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) $

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:

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

  1. $12$

  2. $15$

  3. $25$

  4. $52$

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Correct Option: A
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.

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?

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

  1. $52$ years

  2. $50$ years

  3. $48$ years

  4. $54$ years

Show answer
Correct Option: A
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.