Question 12 Marks
Anamika thought of a number. She multiplied it by $2,$ added 5 to the product and obtained $17$ as the result. What is the number she had thought of $?$
AnswerLet $x$ be number thought by Anamika.
If she multiplied it be $2,$ then the number will be $2x.$
Also, added $5$ to it obtained $17$ as the result.
$\therefore2\text{x}+5=17$
$\Rightarrow2\text{x}=17-5[ $transposing $5$ to $RHS]$
$\Rightarrow\text{x}=\frac{12}{2}=6$
Hence, the number $6$ is thought by Anamika.
View full question & answer→Question 22 Marks
The interest received by Karim is $Rs. 30$ more than that of Ramesh. If the total interest received by them is $Rs. 70,$ find the interest received by Ramesh.
AnswerLet the interest received by Karim be $Rs. x,$
then interst received by Ramesh will be $Rs. (x - 30).$
So, the interest received by both will be $Rs. (x + x - 30).$
According to the question, $x + x - 30 - 70$
$\Rightarrow 2x = 70 + 30 [$transposing $(-30)$ to $RHS]$
$\Rightarrow x = 100$
$\Rightarrow x = Rs. 50 [$dividing both sides by $2]$
So, the interest received by Ramesh $= Rs. (x - 30) = Rs. (50 - 30) = Rs. 20$
View full question & answer→Question 32 Marks
A number is $7$ more than one-third of itself.
AnswerLet the number be $x.$
Then, $\frac{1}{3}\text{rd}$ of the number $=\frac{\text{x}}{5}$
So, the equation formed is $\text{x}=7+\frac{\text{x}}{3}.$
View full question & answer→Question 42 Marks
If $1$ is subtracted from a number and the difference is multiplied by $\frac{1}{2},$ the result is $7.$
AnswerLet the number be $x.$
Then, $1$ is subtracted from a number and the difference is multiplied by $\frac{1}{2}$
i.e, $\frac{1}{2}(\text{x}-1)$
It given result $7.$
So, the equation formed is $\frac{1}{2}(\text{x}-1)=7$
View full question & answer→Question 52 Marks
$150$ has been divided into two parts such that twice the first part is equal to the second part. Find the parts.
AnswerLet one part be $x,$
then other part will be $2x$ as second part is twice the first part.
Since, $150$ has been divided into above two parts.
$\text{x}+2\text{x}=150$
$\Rightarrow3\text{x}=150$
$\Rightarrow\frac{3\text{x}}{3}=\frac{150}{3}$
$[$dividing both sides by $3]$
$\Rightarrow\text{x}=50$
Hence, the first part is $50$ and the second part is $2 × 50 = 100.$
View full question & answer→Question 62 Marks
Follow the directions and correct the given incorrect equation, written in Roman numerals: Move one matchstick to make the equation valid. Find two different solutions. $\ce{VI - IV = XI}$
AnswerGiven, $\ce{VI + IV = XI}$
According to the question, we have top move one mathchstick to make a valid equation.
$i. \ce{VI + IV = X}$
$\Rightarrow 6 + 4 = 10 [$in numerical system$]$
$ii. \ce{VI - V = XI}$
$\Rightarrow 6 + 5 = 11 [$in numerical system$]$
View full question & answer→Question 72 Marks
If one side of a square is represented by $18x - 20$ and the adjacent side is represented by $42 - 13x,$ find the length of the side of the square.
AnswerGiven, one side of square is $18x - 20$ and adjacent side is $42 - 13x.$
We know that, all the sides of a square are always equal.
$\therefore 18x - 20 = 42 - 13x$
$\Rightarrow 18x + 13x = 42 + 20$
$\Rightarrow31\text{x}=62$
$\Rightarrow\text{x}=\frac{62}{31}=2$ units
Hence, side of the square is $(18 \times 2) - 20 = 36 - 20 = 16$ units.
View full question & answer→Question 82 Marks
If $45$ is added to half a number, the result is triple the number. Find the number.
AnswerLet $x$ be the number.
Then half of number is $\frac{\text{x}}{2}.$
According to the question,
$\frac{\text{x}}{2}+45=3\text{x}$
$\Rightarrow\frac{\text{x}+90}{2}=3\text{x}$
$\Rightarrow\text{x}+90=6\text{x}$
$\Rightarrow\text{x}=\frac{90}{5}=18$
View full question & answer→Question 92 Marks
Radha got $Rs. 17,480$ as her monthly salary and over-time. Her salary exceeds the over-time by $Rs. 10,000.$ What is her monthly salary $?$
AnswerRadha's monthly salary and over-time $= Rs. 1780 [$given$]$
Let $Rs. x$ be the her monthly salary.
Then, overtime $= Rs. (x - 1000)$
$\therefore 17480 - x = x - 10000 $
$\Rightarrow 2x = 27480$
$\Rightarrow x = 13740$
Hence. her monthly salary is $Rs. 13740.$
View full question & answer→Question 102 Marks
The age of Sohan Lal is four times that of his son Amit. If the difference of their ages is $27$ years, find the age of Amit.
AnswerLet $x$ year be the age of Amit.
Then, age of Sohan Lal $= 4x$ year
According to the question,
$4\text{x}-\text{x}=27$
$\Rightarrow3\text{x}=27$
$\Rightarrow\text{x}=\frac{27}{3}=9$
Hence, the age of Amit is $9$ year.
View full question & answer→Question 112 Marks
Subramaniam and Naidu donate some money in a Relief Fund. The amount paid by Naidu is $Rs. 125$ more than that of Subramaniam. If the total money paid by them is $Rs. 975,$ find the amount of money donated by Subramaniam.
AnswerLet $Rs. x$ be the amount donated in a Relief fund by Subramaniam.
Then, the amount donated by Naidu will be $Rs. (x + 125).$
According to the question, $x + x + 125 = 975 $
$\Rightarrow 2x = 975 - 125 [$transposing $125$ to $RHS] $
$\Rightarrow 2x = 850 $
$\Rightarrow x = Rs. 425 [$dividing both sides by $2]$
Hence, the amount of money donated by Subramaniam is $Rs. 425.$
View full question & answer→Question 122 Marks
If $10$ is subtracted from half of a number, the result is $4.$
AnswerLet the number be $x.$
Then, $10$ is subtracted from $\frac{\text{x}}{2}$
i.e, $\frac{\text{x}}{2}-10$ and results $4.$
So, the equation formed is $\frac{\text{x}}{2}-10=4.$
View full question & answer→Question 132 Marks
Follow the directions and correct the given incorrect equation, written in Roman numerals: Remove two of these matchsticks to make a valid equation: $IX - VI = V$
AnswerGiven, $IX - VI = V$
According to the question,
we have to remove two matchasticks to make a vaild equation.
Hence, $X - V = V [$in numerical system$] $
$\Rightarrow 10 - 5 = 5$
View full question & answer→Question 142 Marks
One-fifth of a number is $5$ less than that number.
AnswerLet the number be $x.$
Then, $\frac{1}{5}\text{th}$ of the number $=\frac{\text{x}}{5}$
Now, $\frac{\text{x}}{5}$ is $5$ less than $x.$
So, the equation formed is $\frac{\text{x}}{5}=\text{x}-5.$
View full question & answer→Question 152 Marks
Seven times a number is $12$ less than thirteen times the same number. Find the number.
AnswerLet the number be $x.$
Then, seven times of this number $= 7x$ and thirteen times of this number $= 13x.$
According toi the question,
$\Rightarrow 13x - 7x = 12$
$ \Rightarrow 6x = 12 $
$\Rightarrow x = 2 [$dividing both sides by $6]$
Hence, the required number is $2.$
View full question & answer→Question 162 Marks
One of the two numbers is twice the other. The sum of the numbers is $12.$ Find the numbers.
AnswerLet $x$ be the one of the number.
Then, other number is twice the first one $= 2x.$
According to the question, $\text{x}+2\text{x}=12$
$\Rightarrow3\text{x}=12$
$\Rightarrow\frac{3\text{x}}{3}=\frac{12}{3} [$dividing both sides by $3]$
$\Rightarrow\text{x}=4$
Hence, the numbers are $x = 4$ and $2x = 2 \times 4 = 8.$
View full question & answer→Question 172 Marks
A number exceeds the other number by $12.$ If their sum is $72,$ find the numbers.
AnswerLet $x$ be a number, then another number will be $x + 12.$
According to the question, $x + x + 12 = 72$
$\Rightarrow 2x = 72 - 12 [$trasnposing $12$ to $RHS]$
$\Rightarrow 2x = 60$
$\Rightarrow x = 30 [$dividing both sides by $2]$
Hence, the number are $30$ and $(30 + 12)$ i.e, $30$ and $42.$
View full question & answer→Question 182 Marks
The given figure represents a weighing balance. The weights of some objects in the balance are given. Find the weight of each square and the circle.
AnswerWeight on $LHS = 40\ kg$
Weight on $RHS = 14 + 4 = 18\ kg$
Weight should be equal,
Therefore, circle weight $= 40 - 18 = 22\ kg$
View full question & answer→Question 192 Marks
A number divided by $2$ and then increased by $5$ is $9.$
AnswerLet the number be $x.$
Then, $x$ is divided by $2$ and increased by $5,$ i.e,
$\frac{\text{x}}{2}+5$ and given result $9.$
So, the equation formed is $\frac{\text{x}}{2}+5=9$
View full question & answer→Question 202 Marks
Two times a number increased by $5$ equals $9.$ Find the number.
AnswerLet the number be $x.$
It is given that two times this number increased by $5$ equals $9$.
$\therefore 2x + 5 = 9$
$\Rightarrow 2x = 9 - 5$
$\Rightarrow 2x = 4$
$\Rightarrow x = 2$
$[$dividing both sides by $2]$
Hence, the required number is $2.$
View full question & answer→Question 212 Marks
The sum of three consecutive integers is $5$ more than the smallest of the integers. Find the integers.
AnswerLet one number be $x$.
Then, the next two consecutive numbers will be $x + 1$ and $x + 2.$
Sum of these three numbers $= x + (x + 1) + (x + 2) = 3x + 3$
According to the question, $3x + 3 = x + 5$
$\Rightarrow3\text{x}-\text{x}=5-3$
$[$transposing $x$ to $LHS$ and $3$ to $RHS]$
$\Rightarrow2\text{x}=2$
$\Rightarrow\frac{2\text{x}}{2}=\frac{2}{2} [$dividing both sides by $2]$
$\Rightarrow\text{x}=1$
$\therefore$ Hence, the number are $1, 1 + 1, 1 + 2$ i.e, $1, 2, 3.$
View full question & answer→Question 222 Marks
A number when divided by $6$ gives the quotient $6.$ What is the number$?$
AnswerLet the required number be $x.$
Then, $x$ divided by $6=\frac{\text{x}}{6}.$
It is given that when is $x$ is divided by $6,$ gives the quotient as $6.$
So, we obtain the following equation $\frac{\text{x}}{6}=6$
$\Rightarrow\frac{\text{x}}{6}\times6=6\times6[ $multiplying both sides by $6]$
$\Rightarrow\text{x}=36$
Hence, the required number is $36.$
View full question & answer→