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SSC MTS 11 Feb 2026 Shift 2 Paper

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Question : 10 of 90

Marks: +1, -0

If

(9x-3y)=96

4x:3y=20:21

, then find the value of

(2x^{2}+3y^{2})

.

2756
3341
3152
2280

Solution:

Concept:

Use ratio to express variables in terms of a common constant, then solve the linear equation.

Explanation:

Given

4x : 3y = 20 : 21

. Write as

\frac{4x}{3y} = \frac{20}{21}

. Cross-multiply:

4x \cdot 21 = 3y \cdot 20

=>

84x = 60y

=>

\frac{x}{y} = \frac{60}{84} = \frac{5}{7}

. So let

x = 5k

and

y = 7k

.

Substitute into

9x - 3y = 96

:

9(5k) - 3(7k) = 96

=>

45k - 21k = 96

=>

24k = 96

=>

k = 4

.

Thus

x = 5 \times 4 = 20

,

y = 7 \times 4 = 28

.

Now compute

2x^{2} + 3y^{2} = 2(20)^{2} + 3(28)^{2} = 2(400) + 3(784) = 800 + 2352 = 3152

.

Answer:

3152, which corresponds to option C.

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