2x + 3y = 38 and \(\frac{x+y}{y}=\frac{15}{8}\), then find the value of 6x +7y.

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This question was previously asked in

HPCL Engineer Civil 23 Dec 2023 Official Paper

Answer 1

The Given:

2x + 3y = 38 ---(1)

\(\frac{x+y}{y}=\frac{15}{8}\) ---(2)

Calculation:

We have,

\(\frac{x+y}{y}=\frac{15}{8}\)

⇒ 8x + 8y = 15y

⇒ 8x -15y + 8y

⇒ 8x - 7y = 0 --(3)

From equation (1) and (3) -

2x + 3y = 38

8x - 7y = 0

After solving these two equations, we get

x = 7 and y = 8

Now,

6x + 7y

⇒ 6 × 7 + 7 × 8

⇒ 42 + 56 = 98

∴ The correct answer is option (3).

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