Quantitative Reasoning

Linear Equation

Easy

Reena is twice as old as Sunita. Three years ago, Reena was three times as old as Sunita. What is present age of Reena?

✅ Correct Option: 4

Let Sunita's present age $= S$

Let Reena's present age $= R$

Reena is twice as old as Sunita:

$R = 2S$

Three years ago, Reena's age was $R - 3$

Three years ago, Sunita's age was $S - 3$

At that time, Reena was three times as old as Sunita:

$R - 3 = 3(S - 3)$

$R - 3 = 3S - 9$

$R = 3S - 6$

From the two equations:

$R = 2S$

$R = 3S - 6$

Setting them equal:

$2S = 3S - 6$

$2S - 3S = -6$

$-S = -6$

$S = 6$

Sunita's present age is $6$ years.

Using $R = 2S$ :

$R = 2 \times 6$

$R = 12$

Therefore, Reena's present age is $12$ years.

2025: 24 May Shift 2

The equations: x + 4y - 3 = 0 and 2x + 8y - 6 = 0 have

2025: 29 May Shift 1

Which of the following pair of linear equations is inconsistent?

(A) x - y = 5; 3x - 3y = 10

(B) 2x + 3y = 4; 4x + 6y = 8

(D) 2x + 5y = 2; 6x - 15y = 4

Choose the correct answer from the options given below:

2025: 26 May Shift 1

Seven chairs and three tables together cost ₹ 7400, three chairs and five tables together cost ₹ 5400. The total cost (in ₹) of 1 chair and 2 tables is:

2025: 19 May Shift 1

The sum of digits of a two-digit number is 14 and the difference between the two digits of the number is 2. The product of the two digits of the number is:

2025: 14 May Shift 1

Two water pipelines are represented by the equations $kx + 3y +1 = 0$ and $2x + y + 3 = 0$ . For what value of k, the pipelines cross each other?

2026: 18 May Shift 1

Which one of the following pairs of linear equations is/are inconsistent?

(A). $7x + y = 5, 14x + 2y = 10$

(B). $2x - 3y = 7, 4x - 6y = 12$

(C). $x - y = 10, 3x - 3y = 16$

(D). $2x - 2y - 2 = 0, 4x - 4y - 5 = 0$

Choose the correct option from the given below:

Reena is twice as old as Sunita. Three years ago, Reena was three times as old as Sunita. What is present age of Reena?

Solution

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