SarkariPYQ

SSC CGL 2023 PYQ — Question 75

SSC CGL - 24 July 2023 - Shift 1 • Quantitative Aptitude • Q75

Back to paper

The value of p2−(q−r)2(p+r)2−q2+q2−(p−r)2(p+q)2−r2+r2−(p−q)2(q+r)2−p2\frac{p^2-(q-r)^2}{(p+r)^2-q^2}+\frac{q^2-(p-r)^2}{(p+q)^2-r^2}+\frac{r^2-(p-q)^2}{(q+r)^2-p^2} is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 1.

p2−(q−r)2(p+r)2−q2+q2−(p−r)2(p+q)2−r2+r2−(p−q)2(q+r)2−p2\frac{p^2-(q-r)^2}{(p+r)^2-q^2}+\frac{q^2-(p-r)^2}{(p+q)^2-r^2}+\frac{r^2-(p-q)^2}{(q+r)^2-p^2}

⇒ (p + q - r)(p - q + r)/(p + r + q)(p + r - q) + (q - p + r)(q + p - r)/(p + q - r)(p + q + r) + (r - p + q)(r + p - q)/(q + r - p)(q + r + p)

⇒ (p + q - r)/(p + r + q) + (q - p + r)/(p + q + r) + (r + p - q)/(p + q + r)

⇒ (p + q - r + q - p + r + r + p - q)/(p + q + r)

⇒ (2p - p + 2q - q + 2r - r)/(p + q + r)

⇒ (p + q + r)/(p + q + r) = 1