Conversion of Verbal Statements to Equations

Q.

Sunita is twice as old as Ashima. If six years is subtracted from Ashima’s age and four years added to Sunita’s age, then Sunita will be four times Ashima’s age. How old were they two years ago?

Q.

Robert’s father is $4$ times as old as Robert. If after 5 years, father will be three times as old as Robert, then the present age of Robert’s father is:

1. $40$
2. $10$
3. $60$
4. $45$

Q.

The solution of which of the following equations is neither a fraction nor an integer.

1. $3x+2=5x+2$

2. $4x–18=2$

3. $4x+7=x+2$

4. $5x–8=x+4$

Q.

If the cost of a pencil is ₹ $(x+5)$ and that of an eraser is ₹ $x$, then how do we represent the statement:
"The total cost of 5 pencils and 10 erasers is ₹ 100" in the form of a linear equation in $x$?

1. $5x+10x=100$

2. $5(x+5)+10(x+5)=100$

3. $5x+10(x+5)=100$

4. $5(x+5)+10x=100$

Q.

What is the next number in the sequence $100,52,28,16,10,\_\_$.

1. $5$

2. $6$

3. $7$

4. $8$

Q. A pencil costs ₹ 5 more than the cost of an eraser. The total cost of 5 pencils and 10 erasers is ₹ 100. Find the cost of a pencil and the cost of an eraser?

1. Eraser - ₹15
   Pencil - ₹ 10
2. Eraser - ₹ 15
   Pencil - ₹ 20
3. Eraser - ₹ 10
   Pencil - ₹ 15
4. Eraser - ₹ 5
   Pencil - ₹ 10

Q.

7 years hence, Sarosh's father age will be thrice that of Sarosh's age. Presently father's age is 6 times of Sarosh's age. Sum of their present ages is equal to:

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Q.

I have x apples. Now, my friend has six more than 3 times the number of apples I have. How many apples does my friend have?

1. 3x

2. x+6

3. 3x+6

4. 6x

Q. When the numerator is increased by 17 and the denominator is decreased by 1, the fraction obtained is $\frac{3}{2}$. Knowing that the denominator is greater than the numerator by 8, how do we represent the above situation in the form of an equation?

1. $\frac{N+17}{N+7}=\frac{2}{3}$
2. $\frac{N+7}{N+17}=\frac{3}{2}$
3. $\frac{N+17}{N+7}=\frac{3}{2}$
4. $\frac{N+7}{N+17}=\frac{2}{3}$

Q.

One pleasant morning, a number 'a' goes for a jog. Another number 'b' passes by 'a' and comments "I am four more than your half”. 'a' gets offended and starts shouting at 'b'. Now, both of them got into a big fight about their value and soon a big crowd gathered. A wise man, Krishna comes, looks at both the numbers, and says, "If you look closely, you are both equals.” 'a' and 'b' realised that the wise man was correct. What are the numbers 'a' and 'b'?

1. $8,8$
2. $8,4$
3. $4,4$
4. $8,10$

Q.

Ajay is $36$ years older than his son . After $10$ years , Ajay will be three times as old as his son . Find their present ages.

Q.

Raju reads $\frac{2}{3}$ rd of a book. He finds that still there are 100 pages to be read. The total number of pages in the book are?

Q. If ten more than twice a number is 100 then the number is

1. 55
2. 50
3. 45

Q. The ratio of the weight of a box to the weight of the car is 3 : 16. If the car weighs 1600 kg, find the weight of the box.

1. 300 kg
2. 400 kg
3. 600 kg
4. 1000 kg

Q.

If $460m$ of wire is be required for fencing a square garden, then find the side of the garden.

Q.

Pavani has a certain number of chocolates; she gave one-third of the chocolates to her brother Arjun, one-sixth to her friend Preeti. She was then left with 30 chocolates. What is the sum of the number of chocolates did she give to Arjun and Preeti?

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Q. The sum of two rational numbers is -3.If one of the number is $\frac{7}{5}$ then what is the other number?

Q. When I say "I am as tall as my brother", which of the following equations I am actually representing?

1. My height = My brother's height
2. My weight = My brother's weight
3. My height > My brother's height
4. My height < My brother's height

Q. My friend has 3 less than twice the number of oranges I have. The ratio $\frac{\text{number of oranges I have}}{\text{number of oranges my friend has}}$ is equal to $\frac{2}{3}$. How many oranges do each of us have?

1. Me - 6.
   My friend - 7.
2. Me - 8.
   ​My friend - 12.
3. Me - 6.
   ​My friend - 9.
4. Me - 10.
   ​My friend - 15.

Q.

While playing cards, Ahmed won $₹79$ in the first game, lost$₹60$ in the second game, again won $₹58$ in the third game, and finally lost$₹113$ in the fourth game. Find his final loss or gain.

Q.

Karan and Kundan are two brothers. Presently Karan's age is four times the age of Kundan. After 6 years Karan's age will be twice as that of Kundan. What is the present age of Kundan?

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Q. Aditya has a certain number of pencils that cost ₹3 per piece. The total cost of all the pencils he had is 10 more than 4 times the number of pencils. If the total cost is ₹162, then how many pencils does Aditya have?

1. 10
2. 12
3. 11
4. 13

Q.

If a certain number when decreased by $21$ becomes $81$, what is the number?

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Q. 64 gold coins must be distributed between 2 people (A and B) such that ${\frac{1}{5}}^{th}$ of the number of gold coins received by A is equal to ${\frac{1}{3}}^{rd}$ of the number of gold coins received by B. What is the number of gold coins received by A and B?

1. A - 44, B - 20.
2. A - 22, B - 42
3. A - 48, B - 16
4. A - 40, B - 24

Q.

When $75\%$ of a number is added to 75, then resultant number is the original number. The number is

1. 100

2. 45

3. 150

4. 300

Q. When you subtract 3 from eight times a number, you get 5. Find the number.

1. 3
2. 2
3. 4
4. 1

Q. A shopkeeper has an unknown weight in his shop. To find out the weight, he first weighs $1kg$ of rice, and then weighs $1kg$ of rice and the unknown weight together. The combined weight of the rice and the unknown weight is $1.5kg$. Find the unknown weight (in grams).

Q.

Your friend solves the inequality. Is your friend correct? Explain your reasoning.

Q.

Tony scored twice as many runs as Kohli. Together they scored $6$ runs short of triple century. How many runs did each score?

1. $196,98$

2. $96,192$

3. $250,125$

4. $19,38$

Q. Write the correct equation for the statement "You get 4 if 7 is subtracted from 6 times a number".

1. 7x - 6 = 4
2. 6x - 7 = 4
3. 5x - 2 = 8
4. 6x - 4 = 7