Tag: maths

Questions Related to maths

A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both used in the second-half of the time?

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

  1. $15$

  2. $20$

  3. $27.5$

  4. $30$

Show answer
Correct Option: D
Explanation:

Let x minute will be taken. In one minute A can fill the $\dfrac {1}{60}$ part of tanker and in one minute B can fill the $\dfrac {1}{40}$ part.
Both can fill in t
$\dfrac {t}{60}+\dfrac {t}{40}=1$
$t=\dfrac {60\times 40}{100}$
$t=24$
both can fill in one minute $\dfrac {1}{24}$ part of tanker.
$1=\left (\dfrac {x}{2}\right )\dfrac {1}{40}+\dfrac {x}{2}\left (\dfrac {1}{24}\right )$
$1=\dfrac {x}{80}+\dfrac {x}{48}$
$x=\dfrac {80\times 48}{128}=30$

Two birds are flying in opposite directions over the edge of a circle-shaped forest of radius 4 km. Both start off from the same point simultaneously and both have to go to the same nest. Who reaches the nest first?
I. Speed of bird A is 60 km/hr and speed of bird B is 50 km/hr.
II. The nest is diametrically opposite to the starting point of the flight of the two birds, on the circumference of the forest.

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

  1. If the question can be answered by anyone of the statements alone, but cannot be answered by using the other statement alone.

  2. If the question can be answered by using either statement alone.

  3. If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

  4. If the question. cannot be answered even by using both the statements together.

Show answer
Correct Option: D
Explanation:

In the problem statement, the distance is given. 
In the first statement, the speeds are given.
In the second statement, nothing substantial can be concluded.
Since information on the paths of flight is not given, we can not determine which bird reaches first. D,

To find the present age of Rishi, which statements can be dispensed.
I. In ten years,Richard will be twice as old as Rishi was 10 years ago.
II. Richard is now 9 years older than Rishi.
III. Five years ago, Rishi was 9 years younger than Richard.

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

  1. Only II

  2. Only III

  3. Either I or II

  4. None of the three statements can be dispensed with

Show answer
Correct Option: C
Explanation:
There are 2 unkown variables, Rishi's age x and Richard's age y.
Each of the following statements give relation between x and y.

Statement I  says: $\quad y+10=2x.$
Statement II says: $\quad y=x+9$

Statement III says:  $y-5=(x-5)+9$= Statement II.
To solve for 2 unknown we require 2 equations.

Since, Statement II and Statement III are equivalent , either can be dispensed with.

Helen is determining how much money she and her friends will need to go for a movie.
Each person going will buy a ticket, a bag of popcorn, and a drink. Helen writes the given formula that will represent the situation.
$m = q (t + p + d)$
Which description represents the meaning of the variable $q$?

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

  1. The price of a ticket

  2. The cost of concessions

  3. The number of people going

  4. The amount of money required

Show answer
Correct Option: C
Explanation:

From the formula $ m = q \left(t+p+d \right)$
t represent the money required for  each ticket
p represent the money required for popcorn for each person
d represent the money required for drink for each person
If we multiply this with the total no of persons going to watch movie we can get total money require.

A clock is set right at $8:00\ a.m$. The clock gains $10$ minutes in $24$ hours. What will be the right time when this clock indicates $1\ p.m$ on the following day?

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

  1. $11.40\ p.m$

  2. $12:00\ p.m$

  3. $10:00\ p.m$

  4. $12:48\ p.m$

  5. $None\ of\ these$

Show answer
Correct Option: D
Explanation:

The clock gains $10$ mins in $24$ hours,
It will gain 1 min in every $2.4$ hours.
Difference in time the clock indicates=$1$ p.m.-$8$ a.m. (the next day)
=$29$ hours,
Time gained=$\dfrac {29}{2.4}=12$ mins.
Actual time=$12:48$ p.m.

Three years ago, the average age of the family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. What is the baby today?

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

  1. 4 years

  2. 3 years

  3. 2 years

  4. 1 year

Show answer
Correct Option: C
Explanation:

Present total ages of six members $=17\times6$ i.e., 102 years.
Present ages of 5 members $=5\times(17+3)$ i.e. 100 years.
$\implies$ Baby is 2 years old to-day.

Henry just set up direct deposit from his employer to his checking account. The equation $\displaystyle y=360x-126.13$ represents the balance in Henry's account if he deposit his weekly paycheck for x weeks. Based on this equation, which of the following statements is true

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

  1. Henry earns $126.13 per week.

  2. Henry made an initial deposit of $126.13.

  3. Before setting up the direct deposit, Henry had overdrawn his account.

  4. When Henry set up the direct deposit, he already has $360 in his account.

Show answer
Correct Option: C
Explanation:

The balance in Henry's account follows the relation $y = 360x - 126.13$, where $y$ is the balance in Henry's checking account and $x$ is the number of weeks passed. 

The difference in the balance between any two successive weeks is $ $360 $. This shows that Henry earns $ $360$ per week.
The other options can be checked simultaneously. After putting $x = 0$, we get $y = -126.13$. This shows that only option C is correct.

Ajit is $21$ years younger than his father. What is their total age in $7$ years time?

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

  1. $(x + 28)$ years

  2. $(x + 35)$ years

  3. $(2x + 28)$ years

  4. $(2x + 35)$ years

Show answer
Correct Option: D
Explanation:
Let the age of Ajit be $x$ years.
$\therefore$ Age of Ajit's father $= x + 21$
After $7$ years-
Age of Ajit $= (x + 7)$ years
Age of Ajit's father $= x + 21 + 7 = x + 28$
Total age of Ajit and Ajit' father $= x + 7 + x + 28 = (2x + 35)$ years

Reema bought $x$ pens at Rs.$2.60$ each and $y$ greeting cards at $80$ paise each. If the pens cost Rs.$12$ more than the cards, the equation involving $x$ and $y$ is

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

  1. $13x-4y=6$

  2. $13x-4y=60$

  3. $260x-8y=100$

  4. $260x-8y=12$

Show answer
Correct Option: B
Explanation:

Given that Reema bought $x$ pens at Rs. $2.60$ each and $y$ greeting cards at $80$ paise each

Then cost of x pens $ =2.60 x$ RS 
And cost of y greeting cards $=0.80 y$ Rs
But given that total cost of pens is Rs $12$ more than the cards

$\therefore 2.60 x=0.80 y+12$
Mltiply by 10 both sides we get
$2.60x\times 10=0.80y\times 10+12\times 10$
$\Rightarrow 26x=8y+120$
$\Rightarrow 26x-8y=120$
Divided by 2 both sides we get
$13x-4y=60$

Equation for the statement 'Thrice the length ($l$) of a room is $340$ metres' is _____ .

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

  1. $3l=430$

  2. $3l=340$

  3. $3+l=340$

  4. $3l+340=0$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$   The length of room is $l$.

$\Rightarrow$   So, thrice the length means $3l$.
$\therefore$    According to the statement given in question,
$\Rightarrow$  $3l=340$