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UPSC NDA I 2025 Mathematics Paper

Question : 4 of 120

Marks: +1, -0

x+\frac{5}{y}=4

y+\frac{5}{x}=-4

what is (x + y) equal to?

Solution:

Concept:

Eliminate fractions by multiplying each equation by the denominator, then subtract to find the value of

x+y

Explanation:

Start with

x+\frac{5}{y}=4

. Multiply both sides by

y

xy+5=4y

...(1)

Next,

y+\frac{5}{x}=-4

. Multiply both sides by

x

xy+5=-4x

...(2)

Subtract equation (2) from equation (1):

(xy+5)-(xy+5)=4y-(-4x)

0=4y+4x

Divide by 4:

0=x+y

Thus,

x+y=0

Answer:

Option A (0)

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