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

The sum of the digits of a two-digit number is 9 less then the number. Which of the following digits is at unit's place of the number ?

  1. 1

  2. 2

  3. 4

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let $x,y$ are the digits of a number. Then the number $= 10x+y$

as per condition : $10x+y-9 = x+y$

Then as per the given problem,

$x+y=10x+y-9$

or, $9x=9$

or, $x=1$

So, we can say that for any value of y from 1 to 9, the condition satisfies.

for eg: if the number is 18

18–9 = 1+8

9=9 , satisfied.


So the tenth's place digit is $1$.

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

Get the algebraic expression in the following cases using variables, constant and arithmetic operations.
Subtraction of $z$ from $y$.

  1. $y+z$
  2. $y-z$
  3. $z-y$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Subtraction of $z$ from $y$ implies that a number of value $z$ is to be subtracted from another number of $y$ value $y$ which means $y-z$.

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

Two years ago the mean age of $40$ people was $11$ years. Now a person left the group and the mean age is changed to $12$ years, then the age of the person who left the group is?

  1. $52$ years
  2. $48$ years
  3. $54$ years

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of ages 2 years ago = 40*11 = 440. Sum of ages now = 440 + 40*2 = 520. After one person leaves, 39 people have mean age 12, sum = 39*12 = 468. Age of person = 520 - 468 = 52.

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

Five years ago Anjali's age was twice Sarita's age. Five years hence, their ages will be $4 : 3$. Anjali's present age is 

  1. $15$ years
  2. $10$ years
  3. $12$ years
  4. $16$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A and S be current ages. (A-5) = 2(S-5) => A-2S = -5. (A+5)/(S+5) = 4/3 => 3A+15 = 4S+20 => 3A-4S = 5. Solving the system: 2A-4S = -10 and 3A-4S = 5. Subtracting gives A = 15.

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

A game is played by three players. The loser has to triple the money of each of the other players has. Three games are played and each one losses a game. At the end all have the same amount namely $Rs.\ 54$. The amount the first loser has at the begining is

  1. $Rs.\ 120$
  2. $Rs.\ 112$
  3. $Rs.\ 110$
  4. $Rs.\ 90$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Working backwards from the final state where each of the three players has Rs 54 (totaling Rs 162), we reverse the losses. The last loser must have tripled the others' money, meaning we trace the sequence of losses in reverse to find the initial amounts, yielding Rs 110 for the first player.

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

When a two digit number is reversed, the new number is reduced by $63$ and the sum of digits of these individual numbers is $9$. Now, if these numbers are converted into base $'x'$ the larger number becomes $5$ times that of smaller one, then the value of $x$ is :

  1. $36$
  2. $13$
  3. $15$
  4. $8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the two-digit number be 10a + b. Reversing it gives 10b + a, and the problem states 10a + b - (10b + a) = 63, which means a - b = 7. Given the sum of digits a + b = 9, we find a = 8 and b = 1, so the numbers are 81 and 18. Converting to base x gives 81 in base x as 5 times 18 in base x, leading to the equation 8x + 1 = 5(x + 8), which solves to x = 13.

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

A tree, in each year, grows $5\ cm$ less than it grew in the previous year. If it grew half a meter per year, then the height of the tree (in meters), when it ceases to grow, is

  1. $2.50$
  2. $2.00$
  3. $3.00$
  4. $2.75$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The annual growth forms an arithmetic progression with a first term a = 0.50 meters (50 cm) and a common difference d = -0.05 meters (-5 cm). The tree ceases to grow when its annual growth becomes zero or negative, which happens after n terms where 0.50 + (n - 1)(-0.05) <= 0, giving n = 10 years. The sum of this finite arithmetic progression is given by S = n/2 * (2a + (n - 1)d), which calculates to 2.75 meters.