Tag: maths

Questions Related to maths

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. $150$

Show answer
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

Show answer
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. $52$

Show answer
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.

A can do a piece of work in $24$ days. If B is $60\%$ more efficient then the number of days required by B to do the twice as large as the earlier work is-

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

  1. $24$

  2. $36$

  3. $15$

  4. $30$

Show answer
Correct Option: D
Explanation:
According to the question-
A can do a piece of work in $24$ days.
$\therefore$ work done by A in $1$ day  $=\cfrac{1}{24}$
Given that, B is $60 \%$ more efficient, i.e., B can do $60 \%$ more work than work done by A in $1$ day-
Work done by B in $1$ day  $=\cfrac{1}{24} + \cfrac{60}{100} \times {1}{24} = \cfrac{1}{15}$
$\therefore$ number of days required by B to do the same work $= 15 $days
$\therefore$ number of days required by B to do the twice as large as the earlier work  $=2 \times 15 = 30$ days

A and B can do a job in $12$ days, B and C can do it in $16$ days. After A has worked for $5$ days and B has worked for $7$ days, C can finish the rest in $13$ days. In how many days can C do the work alone?

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

  1. $16$ days

  2. $24$ days

  3. $36$ days

  4. $48$ days

Show answer
Correct Option: B
Explanation:

Solution:-

Let the amount of work done by $A, B,$ and $C$ per day be $x, y$ and $z$ respectively.
Case I:-

$A$ and $B$ can do the job in $12$ days.
$\therefore$ work done by $A$ and $B$ in one day  $=\cfrac{1}{12}$
$\Rightarrow \; x + y = \cfrac{1}{12}$
Case II:-
B and C can do the job in $16$ days.
$\therefore$ work done by B and C in one day  $=\cfrac{1}{16}$
$\Rightarrow \; y + z = \cfrac{1}{16}$
As given, A has worked for $5$ days and B has worked for $7$ days, C can finish the rest in $13$ days.
$5x + 7y + 13z = 1$
$\Rightarrow$ $5x + 5y + 2y + 2z + 11z = 1$
$\Rightarrow$ $5(x + y) + 2(y + z) + 11z = 1$
$\Rightarrow \; 5 \times \cfrac{1}{12} + 2 \times \cfrac{1}{16} + 11z = 1$
$\Rightarrow \; 11z = 1 - \cfrac{5}{12} - \cfrac{1}{8}$
$\Rightarrow \; 11z = \cfrac{22}{48}$
$\Rightarrow \; z = \cfrac{1}{24}$
Therefore, work done by $C$  $1$ day  $=\cfrac{1}{24}$
Hence, C alone can finish the work in $24$ days.

A thief escaped from police custody. Since he was sprinter he could clock $40\ km/hr$. The police realized it after $3$ hr and started chasing him in the same direction at $50\ km/hr$. The police had a dog which could run at $60\ km/hr$. The dog could run to the thief and then return to the police and then would turn back towards the thief. If kept on doing so till the police caught the thief. Find the total distance travelled by the dog in the direction of the thief.

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

  1. $720 km$

  2. $600 km$

  3. $660 km$

  4. $360 km$

Show answer
Correct Option: C
Explanation:
Speed of thief $=40 \  km \ per\ hr=v _{t}$
Speed of police $=50 \ km\ per\ hr=v _{p}$
Police started after 3hrs of start of thief
$50t=40t+40(3)$
$\therefore   t=12 hr$
Time taken by police to catch thief $=12 hr$
Distance travelled by dog $=12\times 60$
$=720 km$
$\Rightarrow$   Distance travelled by police + To and from distance by Dog $=720$
Distance travelled by police $=50\times 12$
$=600 km$
$\Rightarrow$   $600+2(\text{from distance by dog})=720$
"Fro" distance (distance from thief to police)="to"distance(distance from police to thief after once it returns)
$600+2(\text{'fro' distance by dog})=720$
$\therefore$ 'fro' distance $=60$
$\therefore$ Total distance towards thief $=600+'to"\ distance$
$=720-$ 'fro' distance
$=660 km$

Grass in lawn grown equally thick and in a uniform rate. It takes $24$ days for $70$ cows and $60$ days for $30$ cows to eat the whole of the grass. How many cows are needed to eat the grass in $96$ days?

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

  1. $20$ cows

  2. $24$ cows

  3. $28$ cows

  4. $32$ cows

Show answer
Correct Option: A
Explanation:
Let $n, g, r,$ and $c$ be the no. of cows, grass initially, the rate at which grass grow/day, and grass eaten by cow/day respectively.
Now according to the question-
It takes $24$ days for $70$ cows to eat the whole of the grass.
$g + 24r = 70 \times 24c = 1680c \longrightarrow \left( i \right)$
$g + 60r = 60 \times 30c = 1800c$
Again, given that it takes 60 days for 30 cows to eat the whole of the grass.
$\therefore \; g = 1800c - 60r \longrightarrow \left( ii \right)$
From ${eq}^{n} \left( i \right) \& \left( ii \right)$, we have
$c = \cfrac{3}{10} r \longrightarrow \left( iii \right)$
Now, to eat the grass in 96 days-
$g + 96r = 96 \times nc$
$\Rightarrow \; 96 \times nc = 1800c - 60r + 96r = 1800c + 36r = 1800c + 120c = 1920c$
$\Rightarrow \; n = 20$
Hence, $20$ cows are needed to eat the grass in $96$ days.