RBI OFFICER GRADE ‘B’ PHASE-I EXAM Held on : 09.07.2023(Part-II)

Total Questions: 50

31. In each of the following questions two equations I and II are given. You are required to solve both the equations and

From the questions (31-33)
Give answer (1) if x > y
Give answer (2) if x < y
Give answer (3) if x ≥ y
Give answer (4) if x ≤ y
Give answer (5) if x = y or no relationship between x and y can be established.
I. 15x² + x – 6 = 0
  II. 5y² – 23y + 12 = 0

Correct Answer: (4)
Solution:

I. 15x² + x – 6 = 0
⇒ 15x² + 10x – 9x – 6 = 0
⇒ 5x (3x + 2) – 3 (x + 2) = 0
⇒ (5x – 3) (3x + 2) = 0
⇒ x = ³/₅ or –²/₃
II. 5y² – 23y + 12 = 0
⇒ 5y² – 20y – 3y + 12 = 0
⇒ 5y (y – 4) – 3 (y – 4) = 0
⇒ (5y – 3) (y – 4) = 0
⇒ y = 3/5 or 4
Clearly, x ≤ y

32. Study the above information carefully and answer the questions.

I. 3x² + 29x + 56 = 0
  II. 2y² + 15y + 25 = 0

Correct Answer: (5)
Solution:

I. 3x² + 29x + 56 = 0
⇒ 3x² + 21x + 8x + 5 = 0
⇒ 3x (x + 7) + 8(x + 7) = 0
⇒ (3x + 8) (x + 7) = 0
⇒ x = -8/3 , -7 = -2.67 or -7
II. 2y² + 15y + 25 = 0
⇒ 2y² + 10y + 5y + 25 = 0
⇒ 2y (y + 5) + 5 (y + 5) = 0
⇒ (y + 5) (2y + 5) = 0
⇒ y = -5 or -5/2 = -5 or -2.5

33. Study the above information carefully and answer the questions.

I. 3x² – 14x + 15 = 0
  II. 15y² – 34y + 15 = 0

Correct Answer: (4)
Solution:

I. 3x² - 14x + 15 = 0
⇒ 3x² - 9x - 5x + 15 = 0
⇒ 3x (x - 3) - 5(x - 3) = 0
⇒ (3x - 5) (x - 3) = 0
⇒ x = 5/3 or 3 = 1.67 or 3
II. 15y² - 34y + 15 = 0
⇒ 15y² - 25y - 9y + 15 = 0
⇒ 5y (3y - 5) - 3 (3y - 5) = 0
⇒ (3y - 5) (5y - 3) = 0
⇒ y = 5/3 or 3/5 = 1.67 or 0.6
Clearly, x ≤ y

34. Three men A, B, and C run at respective speeds of 6, 8 and 12 metre per minute. When A, B and C start running around a circular field with circumference 144 metre at the same time from the same point, after how much time will they meet again at the same point for the first time?

Correct Answer: (2) 72 minutes
Solution:

Time = Distance / Speed
Time taken by A to complete
one round = 144 / 6 minutes
= 24 minutes
Time taken by B to complete
one round = 144 / 8 minutes
= 18 minutes
Time taken by C to complete
one round = 144 / 12 minutes
= 12 minutes
∴ Required time
= LCM of 24, 18 and 12 minutes
= 72 minutes

35. 3 balls are randomly drawn from the box in which there are 4 tennis ball, 6 season and 8 dues balls. What is the probability that the balls are different from each other ?

Correct Answer: (2) 4/17
Solution:

Total possible outcomes =
Selection of 3 balls out of 18 balls = ¹⁸C₃
= [18 × 17 × 16] / [3 × 2 × 1] = 816
Favourable outcomes
= 4 × 6 × 8 = 192
(as 1 tennis ball, 1 season ball, and 1 dues Ball are selected)
Required probability = Favourable outcomes / Total possible outcomes
= 192 / 816 = 4 / 17

36. 5 males and 6 females can complete a certain work in 7 days. If, 8 males and 6 females can do a piece of work in 5 days, then how many days will a female take to do the job, if she works alone?

Correct Answer: (2) 126 days
Solution:

According to the question,
(5M + 6W) × 7 = (8M + 6W) × 5
⇒ 35M + 42W = 40M + 30W ⇒ (40 – 35)M = (42 – 30)W
⇒ 5M = 12W
∴ 5M + 6W = (12 + 6)W = 18W
∴ Time taken by 18 women = 7 days
∴ Time taken by 1 woman = 18 × 7 = 126 days

37. What is the circumference of a semicircle, whose diameter is equal to the radius of a hemisphere having total surface area 7392 square cm ?

Correct Answer: (5) 72 cm
Solution:

Total surface area of hemisphere = 3πr² = 7392

Here, the diameter of the semicircle = radius of the hemisphere = 28 cm
Radius of the semicircle
= 28/2 = 14 cm
Circumference of the semicircle = πr + 2r = (22/7)14 + 28 = 72 cm

38. The average age of board of directors of ABC Ltd having 15 directors was 48 years. When a director aged 56 resigned from the board of directors and another director Mr. X retired on the same day, a new director aged 36 years joined in the board of directors. The average age of all 14 directors is found to be 48 years for the next year. What was the age of Mr. X at the time of retirement?

Correct Answer: (5) 42 years
Solution:

Total age = average age × number of members
= 48 × 15 = 720 years
After two directors leave and one joins,
Total age of 14 directors after 1 year = 14 × 48 = 672 years
∴ 720 – 56 – x + 36 + 14 = 672
⇒ 714 – x = 672
⇒ x = 714 – 672
= 42 years
= Age of Mr. X.

39. A truck running on a highway crossed a man walking at the rate of 12 km/h in the same direction. The man could see the truck running for 2 minutes up to 500 metres. What is the speed of the truck?

Correct Answer: (2) 27 km/h 
Solution:

Truck and man are running in the same direction.
If speed of truck = x kmph.
Relative speed = (x – 12) kmph.
∴ Distance = Speed × Time
⇒ 500/1000 = (x – 12) × 2/60
⇒ 1/2 × 30 = x – 12
⇒ x = (12 + 15) kmph.
= 27 kmph

40. During the first year, the population of a village increases by 5%. During the second year it diminishes by 5%. At the end of the second year, the population was 31,500. What was the population at the beginning of the first year?

Correct Answer: (5) 31,578
Solution:

Let the population of the village at the beginning of the first year be P.