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SSC CHSL 2023 PYQ — Question 55

SSC CHSL - 17 Aug 2023 - Shift 2 • Quantitative Aptitude • Q55

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In a right-angled triangle PQR, PQ = 5 cm, QR = 13 cm, and ∠P = 90°. Find the value of tan Q - tan R.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 11960\frac{119}{60}.

Apply Pythagoras theorem:

QR² = PQ² + PR²

13² = 5² + PR²

169 = 25 + PR²

PR² = 144 → PR = 12 cm

Now:

tan Q = opposite/adjacent = PR/PQ = 12/5

tan R = PQ/PR = 5/12

So,

tan Q − tan R = 12/5 − 5/12

= (144 − 25) / 60

= 119 / 60