MAT (Stage-1) Mock Test

Result

MAT (Stage-1) Mock Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is the smallest number, which when divided by 20, 30, 40 and 50, leaves remainders 8, 18, 28 and 38, respectively?

A
488

B
588

C
688

D
788

Solution

As difference between (20 - 8) = (30 - 18) = (40 - 28) = (50 - 38) = 12
So, required number = LCM (20, 30, 40, 50) - 12 = 600 - 12 = 588
Question 2
1 / -0

Find the profit gained in the two transactions if a person sells 2/3 of a product with a profit of 20% and rest of the product at the cost price.

A
10%

B
13.33%

C
15%

D
12.50%

Solution

Let the product quantity be 3i.
Let the cost price of this quantity of product be 3c.
As, 2i of product is sold at a profit of 20%, the cost of which is 2c, sales revenue for 2i of product = 1.2 x 2c = 2.4c.
Now, i of the product is sold at c.
Thus, total sales revenue of the product = 2.4c + c = 3.4c.
So, profit % = (3.4c - 3c)/3c x 100% = (0.4/3) x 100% = 13.333%
Question 3
1 / -0

In a simultaneous roll of two dice, the probability of getting a total of 7 is

A
1/7

B
7/36

C
1/4

D
1/6

Solution

Total number of possible outcomes = (6)² = 36
Favourable cases = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6
Required probability = 6/36 = 1/6.
Question 4
1 / -0

A train, 150 metres long, passes through a tunnel at a rate of 72 kmph in 20 seconds. What is the length of the tunnel?

A
200 m

B
225 m

C
230 m

D
250 m

Solution

Speed of the train = 72 kmph = 72 x 5/18 = 20 m/s
Let L be the length of the tunnel in metres.
Then, 20 = (150 + L)/20 or L = 250 metres
Hence, length of tunnel = 250 metres
Question 5
1 / -0

A train, 350 m long, travelling at a speed of 120 kmph crosses a platform in 24 sec. A man going at a certain speed crosses the platform in 3 min. What is the speed of the man?

A
6 kmph

B
7 kmph

C
8 kmph

D
9 kmph

Solution

Let the length of the platform be x m.
Given, length of the train = 350 m
Distance travelled = (x + 350) m
Time taken = 24 s
Speed in mps = 120 × (5/18) mps = (100/3) mps
Distance = Speed × Time
x + 350 = (24 × 100/3)
x + 350 = 800
x = 450
Speed of the man = Distance/Time
Distance = 450 m
Time = 3 × 60 s = 180 s
Speed of the man = 450/180 mps = 5/2 mps = (5/2) × (18/5) kmph = 9 kmph