Exams › SSC CGL (Prelims) › General

Two chords PQ and RS of a circle intersect at point T. Given PT : TQ = 3 : 4 and RT : TS = 6 : 5, with PQ = p and RS = q, which relation must hold?

1. p^2/q^2 = 147/242
2. p/q = 7/11
3. p^2/q^2 = 245/242
4. p/q = 12/11

Correct answer: p^2/q^2 = 245/242

Solution

By the intersecting chords theorem PT x TQ = RT x TS. Writing PQ = 7k (PT=3k, TQ=4k) and RS = 11m (RT=6m, TS=5m): 12k^2 = 30m^2, so k^2/m^2 = 30/12 = 5/2. Then p^2/q^2 = 49k^2/121m^2 = 49 x 5 / (121 x 2) = 245/242.

Related SSC CGL (Prelims) General questions

• A shopkeeper sells rice at a discount of 6% on the marked price but uses a weight that is 25% less than the actual weight. Find his overall profit percentage.
• The profit made on an article sold for ₹2400 is equal to the loss incurred when it is sold for ₹2000. What will be the profit or loss percentage if the article is sold for ₹2200?
• Train A leaves Station X at 5:00 AM at 50 km/h. Train B leaves Station Y at 7:30 AM at 80 km/h. Both trains move towards each other. The distance between the stations is 500 km. When do they meet?
• A wholesaler marks up goods by 50% and gives a 12% trade discount. A retailer marks up by 20% and offers an 8% discount. The customer pays ₹12,216. What is the wholesaler's cost price approximately?
• If A : B = 3 : 4, B : C = 5 : 6, and C : D = 7 : 8, then find B : D.
• What is the result of $3^2 + 5 \div 0.8$?

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →