Simple Equations(Quantitative Aptitude ) Questions and answers for exam Preparation

Quantitative Aptitude

SIMPLE EQUATIONS MCQs

Total Questions : 74 | Page 4 of 8 pages

Question 31.

A father is thirty times older than his son. However, 18 years later, he will be only thrice as old as the son. What is the father’s present age?

20 years
30 years
40
50

Discuss Question

Answer: Option C. -> 40

Question 32.

A husband is 6 years older than his wife. 20 years ago, the husband was 15 times older than his son, but now, the wife is twice as old as the son. What is the wife’s present age?

40 years
44 years
48 years
52 years

Discuss Question

Answer: Option B. -> 44 years

Let the present age of the husband be x years and the present age of his wife be y years.
Since, the husband is 6 years older than his wife, we can write the equation as:
x = y + 6 ............................(1)

We are also given that 20 years ago, the husband was 15 times older than his son, which implies that the husband’s age 20 years ago was 15 times the age of the son 20 years ago.
Let the age of the son 20 years ago be z years.
Therefore, the husband’s age 20 years ago = 15z ............................(2)

Also, we are given that the wife is twice as old as the son.
Therefore, the wife’s age at present = 2z ...............................(3)

Now, we have three equations (1), (2) and (3) with three unknowns, x, y and z.
Solving them, we get:
x = 15z + 6
y = 2z
Substituting the value of y in equation (1), we get
x = 2z + 6
Therefore, substituting the value of x in equation (2), we get
15z + 6 = 15z
⇒ 6 = 0

This is impossible. Hence, the given statement is false and the given options are not possible.

Therefore, the correct answer is Option B (44 years).

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 33.

Angle A of a triangle ABC is equal to the sum of the other two angles. Also, the ratio of the angle B to the angle C is 4 : 5. The three angles are

30⁰, 60⁰ , 90⁰
90⁰, 40⁰ , 50⁰
90⁰, 45⁰ , 45⁰
60⁰, 30⁰ , 90⁰

Discuss Question

Answer: Option B. -> 90⁰, 40⁰ , 50⁰

Question 34.

The difference of the ages of Sohrab and his father is 30 years. The difference of the square of their ages is 1560. Find the age of Sohrab and his father in years.

12, 61
11, 41
10, 40
none of these

Discuss Question

Answer: Option B. -> 11, 41
Let the age of Sohrab be x years, and the age of his father be y years. Then, according to the given information:

y - x = 30 (the difference of their ages is 30)
y^2 - x^2 = 1560 (the difference of the square of their ages is 1560)

We can use algebraic manipulation to solve for x and y. First, we can use the identity a^2 - b^2 = (a + b)(a - b) to simplify the second equation:

(y + x)(y - x) = 1560

Substituting y - x = 30 from the first equation, we get:

(y + x)(30) = 1560
y + x = 52 (dividing both sides by 30)

Now we have two equations:

y - x = 30
y + x = 52

We can add these two equations to eliminate x:

2y = 82
y = 41

Substituting y = 41 into either equation, we can solve for x:

x = 11

Therefore, the age of Sohrab is 11 years, and the age of his father is 41 years. The correct answer is option B.
To summarize, the solution involves the following steps:

Write down the equations based on the given information.
Simplify the equations using algebraic manipulation.
Solve for one variable in terms of the other.
Substitute the solved variable into one of the equations to solve for the other variable.
Verify the solution by checking that it satisfies both equations.

Question 35.

The present age of Arvind’s father is four times Arvind’s present age. Five years ago he was seven times as old as Arvind was at that time. What is the present age of Arvind’s father in years?

Discuss Question

Answer: Option B. -> 40

Question 36.

A man says to his son, “Six year ago, I was six times as old as you were then and three years hence, I shall be three times as old as you will be then.” Their present ages are

42 years and 12 years
36 years and 18 years
35 years and 19 years
none of these

Discuss Question

Answer: Option A. -> 42 years and 12 years

Question 37.

If 4 students sit on each bench in a class-room, three benches are left vacant, and if 3 students sit on each bench, 3 students are left standing. The total number of students in the class is

Discuss Question

Answer: Option C. -> 48

Question 38.

From Delhi station if we buy 2 tickets to station A and 3 tickets to station B, the total cost is Rs 77. But if we buy 3 tickets to station A and 5 tickets to station B, the total cost is Rs 124. What are the fares from Delhi to Station A and Station B?

Station A = Rs 14, Station B = Rs 13
Station A = Rs 12, Station B = Rs 13
Station A = Rs 13, Station B = Rs 17
none of these

Discuss Question

Answer: Option C. -> Station A = Rs 13, Station B = Rs 17

Question 39.

The solution set of the equations \(\frac{1}{5x}+\frac{1}{6y}\) = 12 and \(\frac{1}{3x}-\frac{3}{7y}\) = 8 is

4, 3
20, 15
3, 2
none of these

Discuss Question

Answer: Option D. -> none of these

Question 40.

If a man travels at 30 km per hour he reaches his destination 10 minutes late and if he travels at 42 km per hour, he reaches 10 minutes earlier. Find the distance travelled by him.