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Q:

Three cars A, B and C started from a point at 5 pm, 6 pm and 7 pm respectively and travelled at uniform speeds of 60 km/hr, 80 km/hr and x km/hr respectively in the same direction. If all the three met at another point at the same instant during their journey, then what is the value of x?

A) 120	B) 110
C) 105	D) 100

Answer & Explanation Answer: A) 120

Explanation:

Distance covered by A till 6pm = 60 km

Distance covered by A till 7 pm = 120 km

Time taken by B to catch A = 60/(80-60 ) = 3 hrs

So A and B will meet at 6pm + 3 hrs = 9pm

Since we know that all three met at the same time

The time taken by C to cover 120 km

difference will be = 9pm –7pm = 2hrs

Therefore,(x –60 )*2 = 120x = 120 km/hr

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Filed Under: Time and Distance
Exam Prep: Bank Exams

Q:

How many pairs (A, B) are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd?

A) 5	B) 6
C) 9	D) 11

Answer & Explanation Answer: A) 5

Explanation:

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Filed Under: Numbers
Exam Prep: Bank Exams

Q:

What is $0.53 + 0.53$ equal to ?

A) 1.068	B) 1.072
C) 1.082	D) 1.096

Answer & Explanation Answer: A) 1.068

Explanation:

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Q:

What is the value of $\sin^{6} θ + \cos^{6} θ + 3 \sin^{2} θ \cos^{2} θ - 1$ ?

A) 0	B) 1
C) 2	D) 4

Answer & Explanation Answer: A) 0

Explanation:

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

What is the value of $\sin^{2} 25 ° + \sin^{2} 65 °$ ?

A) 0	B) 1
C) 2	D) 4

Answer & Explanation Answer: B) 1

Explanation:

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Q:

If 3 tan θ = cot θ where $0 < θ < π / 2$ , then what is the value of θ ?

A) π/6	B) π/4
C) π/2	D) 1

Answer & Explanation Answer: A) π/6

Explanation:

3tan θ = cot θ

3tan θ = 1/tan θ

tan2θ = 1/3

tan θ = 1/√3

θ = π/6

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Q:

There are two parallel streets each directed north to south. A person in the first street travelling from south to north wishes to take the second street which is on his right side. At some place, he makes a 150 deg turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60 deg and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?

A) 7.5 km	B) 10.5 km
C) 12.5 km	D) 15 km

Answer & Explanation Answer: C) 12.5 km

Explanation:

Initially the person is travelling from south to north i.e. D to A

He takes 150 deg right turn and moves AB distance and then he takes 60 deg left turn travels BC

AB = 20km/hr * 15/60 hr = 5km

BC = 30 * 20/60 = 10 km

We know that distance between both the streets is DC = DB + BC

DB = AB cos 60o= 5. ½ =2.5 km

So the distance between streets = 12.5 km

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Filed Under: Height and Distance
Exam Prep: Bank Exams

Q:

Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?

A) 1:√3	B) 1:3
C) 1:2	D) 1:2√3

Answer & Explanation Answer: B) 1:3

Explanation:

Let the side of regular hexagon be ‘a’

Let height of the tower 1 be h1 and tower 2 be h2

Height of tower 1 = h1 = (distance between A and B)* (tan 30o)= a.1/√3

Distance between A and C = 2*√3.a/2= √3a

Height of tower 2 = h2 = (distance between A and C)* (tan 45o) = √3a.1 = √3a

Ratio of height of towers at B and C respectively =a/√3/√3a = 1/3.

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Filed Under: Simplification
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