Quantitative Reasoning

Linear Equation

Medium

Match List - I with List - II.

List - I List - II
(1) $14 - \frac{1}{10}(x+3) = \frac{5}{6}x$ (I) 4
(2) $(x-5)^2 - (x+3)^2 = 48$ (II) $-\frac{23}{2}$
(3) $6(x-4) = 4(x-3) - (3x-8)$ (III) 61
(4) $(2x-1)(2x+3) = (2x-7)(2x+7)$ (IV) $-2$

Choose the correct answer from the options given below:

List - I	List - II
(1) $14 - \frac{1}{10}(x+3) = \frac{5}{6}x$	(I) 4
(2) $(x-5)^2 - (x+3)^2 = 48$	(II) $-\frac{23}{2}$
(3) $6(x-4) = 4(x-3) - (3x-8)$	(III) 61
(4) $(2x-1)(2x+3) = (2x-7)(2x+7)$	(IV) $-2$

(1)-(I), (2)-(II), (3)-(III), (4)-(IV)

(1)-(II), (2)-(I), (3)-(III), (4)-(IV)

(1)-(III), (2)-(IV), (3)-(I), (4)-(II)

(1)-(III), (2)-(IV), (3)-(II), (4)-(I)

✅ Correct Option: 3

Eq (3): $6(x-4) = 4(x-3) - (3x-8) \Rightarrow 6x-24 = x - 4 \Rightarrow x = 4$ (I). Eq (2): $(x-5)^2 - (x+3)^2 = -16x + 16 = 48 \Rightarrow x = -2$ (IV). Eq (4): $4x^2+4x-3 = 4x^2 - 49 \Rightarrow x = -23/2$ (II). Eq (1) therefore maps to III (61). Match: (1)-(III), (2)-(IV), (3)-(I), (4)-(II).

2026: 31 May Shift 2

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

A. x – y = 8, 6x – 6y = 32

B. x + y = 5, 4x + 4y = 20

C. 4x– 6y = 16, 8x – 12y = 18

D. 4x – 4y – 4 = 0, 8x – 8y – 10 = 0

Choose the correct answer from the options given below:

2023: 21 May Shift 1

A railway half-ticket costs half the full ticket. However the reservation charge for all the tickets is constant. One full reserved ticket for a journey is Rs.525. If the cost of one full and one half reserved ticket for the same journey is Rs.850, then what is the reservation charge per ticket?

2022: 8 Aug Shift 1

The value of 'y' in the question $2x + 3y - 7 = 0$ if $x = -3/2$

2026: 14 May Shift 2

Solve the linear equation for $x$ :

$3x - 7 = 2x + 5$

2025: 3 June Shift 1

Read the information given below carefully and answer the question that follows:

Aditi, a salesgirl is appointed at a basic salary of ₹ 1200 per month. The condition of employment further stated that for every sale of ₹ 10000 or above she does, she will get 50 % of basic salary and 10 % of the sales as special incentive. However, this incentive scheme shall not work on the first ₹ 10000 of sales made. What should be the value of sales if Aditi wants to earn ₹ 7600 in a particular month?

2025: 28 May Shift 2

Find the value of p for which the lines, $px + 3y + 5 = 0$ and $8x + 2y - 3 = 0$ are parallel.

Solution

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