Quantitative Reasoning

Linear Equation

Medium

Five years ago, Sanjana was thrice as old as Sanjay. Ten years later, Sanjana will be twice as old as Sanjay. The age of Sanjay and Sanjana are respectively

A. 20

B. 30

C. 40

D. 50

Choose the correct answer from the options given below:

A and D only

A and C only

B and D only

B and C only

✅ Correct Option: 1

Let present ages be $x$ for Sanjana and $y$ for Sanjay.

$x-5=3(y-5)\Rightarrow x=3y-10$ .

$x+10=2(y+10)\Rightarrow 3y-10+10=2y+20\Rightarrow y=20$ , so $x=50$ .

Sanjay is 20 and Sanjana is 50, i.e. A and D.

2023: 30 May Shift 3

An equation of the type $y = kx$ (k $\neq$ 0) represents a line :

2025: 27 May Shift 1

For what value of k, the system of equations $3x - ky - 3 = 0$ and $2x - 3y - 4 = 0$ has no solution?

2022: 6 Oct Shift 1

Match List I with List II

Choose the correct answer from the options given below:

2022: 6 Aug Shift 1

The value of x in the equation $2x - 3 = 7 - 3x$

2026: 6 June Shift 1

Which of the following pair of linear equations is / are 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: 29 May Shift 1

The present ratio of ages of P and Q is 2:7. Six years ago, this ratio was 1:5. Determine the present age of P?

Solution