Tag: forming equations from statements

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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.

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

If a number, when divided by $4$, is reduced by $21$, the number is:

  1. $18$
  2. $20$
  3. $28$
  4. $38$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let $x$ be the number.
If a number is divided by the $4$ the expression becomes $\dfrac{x}{4}$
If a number, when divided by $4$, is reduced by $21$, then the equation is
$\dfrac{x}{4}=x-21$
$\Rightarrow\,\dfrac{x}{4}-x=-21$
$\Rightarrow\,\dfrac{x-4x}{4}=-21$
$\Rightarrow\,-3x=-21\times 4$
$\Rightarrow\,x=\dfrac{21}{3}\times 4=7\times 4=28$
$\therefore\,$,the number is $28$
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The product of two numbers is 1296. If one number is 16 times the other, then the two numbers are 

  1. 144, 25

  2. 81, 49

  3. 144, 9

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the first number be $x$. Then, other number is $16x$.


Now, $x \times 16x =1296$

$16x^2=1296$
$x^2=81$
$x=9$
$16x=16\times 9=144$

Thus, the two numbers are $9$ and $144.$

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

The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of mother is excluded. How old is the mother?

  1. 40 years

  2. 42 years

  3. 48 years

  4. 50 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The average age of the mother and her 6 children (7 people total) is 12 years, meaning their total age is 7 * 12 = 84 years. When the mother is excluded, the average of the 6 children drops by 5 years to 12 - 5 = 7 years, making the total age of the children 6 * 7 = 42 years. Subtracting the children's total age from the family's total age gives the mother's age as 84 - 42 = 42 years.

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

Two years ago, a father was five times as old as his son. Two years later, father age will be 8 more than three times the age of the son. Find the sum of present ages of father and son.

  1. 62 years

  2. 52 years

  3. 42 years

  4. 34 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let F and S be the present ages of the father and son. Two years ago, F - 2 = 5(S - 2), which simplifies to F - 5S = -8. Two years later, F + 2 = 3(S + 2) + 8, which simplifies to F - 3S = 12. Solving these simultaneous equations gives S = 10 and F = 42, so the sum of their present ages is 42 + 10 = 52 years.

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

If $50$ is subtracted from two-third of a number, the result is equal to sum of $40$ and one-fourth of that number. What is the number? 

  1. $174$
  2. $216$
  3. $246$
  4. $336$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number be N. According to the problem, (2/3)N - 50 = 40 + (1/4)N. Rearranging terms gives (2/3)N - (1/4)N = 90. Finding a common denominator results in (5/12)N = 90, which means N = 90 * 12 / 5 = 216.