RBI GRADE ‘B’ OFFICER’S EXAM Held on : 06.02.2011 (Part-III)

Total Questions: 50

1. In a college, the ratio of boys to girls is 31: 23 respectively When 75 more girls join the college, this ratio becomes 124: 107. How many more girls should join the college to make the number of boys and girls equal?

(1) 75
(2) 90
(3) 60
(4) 85
(5) None of these

Correct Answer: (4) 85

Solution:Original number of boys in the college = 31

x

Original number of girls = 23 $x$

$23 x + 75 31 x = 107 124$

$\Rightarrow 2852 x + 9300 = 3317 x$

$\Rightarrow 3317 x - 2852 x = 9300$

$\Rightarrow 465 x = 9300$

$\Rightarrow x = 9300 = 20$

∴ Number of boys = $31 \times 20$ = 620

New number of girls = $23 \times 20 + 75 = 535$

∴ Required answer = $620 - 535 = 85$

2. The compound interest accrued on an amount at the end of two years at the rate of 1 p.c.p.a is 2,862. What is the amount?

(1) 11,250
(2) 12,200
(3) 13,500
(4) `10,000
(5) None of these

Correct Answer: (1) 11,250

Solution:If the principal be Rs. P, then

3. A 280 metres long train travelling at a uniform speed, crosses a platform in 60 seconds and a man standing on the platform in 20 seconds What is the length of the platform ?

(1) 640 metres
(2) 420 metres
(3) 280 metres
(4) Cannot be determined
(5) None of these

Correct Answer: (5) None of these

Solution:When a train crosses a plat- form it covers a distance equal to the sum of lengths of platform and train. Let the length of platform be

x

metre.

∴ Speed of train

4. A triangle has two of its angle in the ratio of 1: 2. If the measure of one of its angles i 30 degrees, what is the measure of the largest angle of the triangle in degrees ?

(1) 100
(2) 90
(3) 135
(4) Cannot be determined
(5) None of these

Correct Answer: (4) Cannot be determined

Solution:If the angle be

3 0°

, then according to ratio,

Second angle = $6 0°$

∴ Third angle = $18 0° - 6 0° - 3 0°$ = $9 0°$

If the given ratio be of two other angles, then

$x + 2 x = 18 0° - 3 0° = 15 0°$ $\Rightarrow 3 x = 15 0° \Rightarrow x = 5 0°$

∴ Second angle = $2 \times 50 = 10 0°$

Hence, the largest angle = $9 0^{\circ}$ or $10 0°$

5. In how many different ways can the numbers '256974' be arranged, using each digit only once in each arrangement, such that the digits 6 and 5 are at the extreme ends in each arrangement?

(1) 48
(2) 720
(3) 36
(4) 360
(5) None of these

Correct Answer: (1) 48

Solution:Four empty places can be filled by 2, 9, 7, and 4 in 4! i.e.

4 \times 3 \times

2 \times 1 = 24

ways.

Case II, [5] [ ] [ ] [6]

Number of arrangements = 24

∴ Required number of arrangements = $24 + 24 = 48$

6. Study the given information carefully and answer the questions that follow:

An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If two marbles are picked at random, what is the probability that both are green?

(1) 2/15
(2) 1/15
(3) 2/7
(4) 1
(5) None of these

Correct Answer: (5) None of these

Solution:Total number of marbles in the
urn = 15

P(S) = Total possible outcomes
= Selection of 2 marbles at random out of 15 marbles

∴ Required probability

P(E)/P(S) = 1/105

7. Study the given information carefully and answer the questions that follow:

An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If three marbles are picked at random, what is the probability that two are blue and one is yellow?

(1) 2/15
(2) 6/91
(3) 12/19
(4) 3/15
(5) None of these

Correct Answer: (3) 12/19

Solution:

8. Study the given information carefully and answer the questions that follow:

An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If four marbles are picked at random, what is the probability that at least one is yellow ?

(1) 91/123
(2) 69/91
(3) 125/143
(4) 1/4
(5) None of these

Correct Answer: (2) 69/91

Solution:

∴ P(E) = Selection of 4 marbles
out of 11 marbles

∴ Required probability

9. Study the given information carefully and answer the questions that follow:

An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If two marbles are picked at random, what is the probability that either both are red or both are green ?

(1) 3/5
(2) 4/105
(3) 2/7
(4) 5/91
(5) None of these

Correct Answer: (2) 4/105

Solution:

∴ Required probability = 4/ $105$

10. Study the given information carefully and answer the questions that follow:

An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If four marbles are picked at random, what is the probability that one is green, two are blue and one is red ?

(1) 4/15
(2) 17/280
(3) 6/91
(4) 11/15
(5) None of these

Correct Answer: (3) 6/91

Solution:

∴ Required probability = $P(E)$ / $P(S)$

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RBI GRADE ‘B’ OFFICER’S EXAM Held on : 06.02.2011 (Part-III)

1. In a college, the ratio of boys to girls is 31: 23 respectively When 75 more girls join the college, this ratio becomes 124: 107. How many more girls should join the college to make the number of boys and girls equal?

2. The compound interest accrued on an amount at the end of two years at the rate of 1 p.c.p.a is 2,862. What is the amount?

3. A 280 metres long train travelling at a uniform speed, crosses a platform in 60 seconds and a man standing on the platform in 20 seconds What is the length of the platform ?

4. A triangle has two of its angle in the ratio of 1: 2. If the measure of one of its angles i 30 degrees, what is the measure of the largest angle of the triangle in degrees ?

5. In how many different ways can the numbers '256974' be arranged, using each digit only once in each arrangement, such that the digits 6 and 5 are at the extreme ends in each arrangement?

6. Study the given information carefully and answer the questions that follow:

7. Study the given information carefully and answer the questions that follow:

8. Study the given information carefully and answer the questions that follow:

9. Study the given information carefully and answer the questions that follow:

10. Study the given information carefully and answer the questions that follow:

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