SSC CHSL 2023 PYQ — Question 70

SSC CHSL - 07 Aug 2023 - Shift 3 • Quantitative Aptitude • Q70

In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank. When Mr. Smith went to a restaurant one day, he left his coat near the door. There was (1)________ in the pockets when he left it, so he was very surprised when he took his coat after his meal and found the (2)________ full of jewellery. There was a waiter near the door, so Mr. Smith said to him, “Somebody has made a mistake. He has put some (3)________ in my coat. Take it, and when he comes back, give it to him.” The waiter took it and went away. Suddenly another man came in with a (4)________ just like Mr. Smith’s. “I am sorry,” said the man , “I made a mistake. I took your coat and you have got mine. Please give me my coat and jewellery.” Mr. Smith answered.” I gave the jewellery to the waiter. He will give it to you.” Mr. Smith called the manager of the restaurant; but the manager said, “We have (5)________ waiters here. We have only waitresses.” “You gave the jewellery to a thief!” shouted the other man. “I shall send for the police!” Mr. Smith paid the man a lot of money for the jewellery.

Find the distance (in cm) between the centres of two circles having radii of 40 cm and 30 cm, respectively, if the length of a/an transverse/indirect common tangent to the two circles is given as 1015\sqrt15cm.

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 80.

Let the distance between the centers be d cm.

Transverse common tangent = d2−(r1+r2)2\sqrt{d^2 - (r_1 + r_2)^2}

where d is distance between the centers, r1 and r2 are the radius of the two circles.

According to the given question,

1015=d2−(40+30)210\sqrt{15} = \sqrt{d^2 - (40 + 30)^2}

⇒ d2 - 4900 = 1500

⇒ d2 = 6400

⇒ d2 = 80