Online Aptitude Test - Aptitude Test - Random

We need to know the S.I., principal and time to find the rate.

Since the principal is not given, so data is inadequate.

Let the speed of the train be x metres/sec.

Time taken to cross a tree =	Length of the train
	Speed of the train

Time taken to cross a platform =	(Length of the train + Length of the Platform)
	Speed of the train

I gives, 13 =	l	13x.
	x

II gives 27 =	l + 250
	x

	13x + 250	= 27
	x

x =	125	m/sec.
	7

Thus I and II give the speed of the train.

The correct answer is (A.)

2 x 5 = 10.

Sum of decimal places = 4

0.002 x 0.5 = 0.001

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

B's 1 day's work =	1	.
	12

A's 1 day's work =	1	; (2 times of B's work)
	6

(A + B)'s 1 day's work =		1	+	1		=	3	=	1	.
		6		12			12		4

So, A and B together can finish the work in 4 days.

Let S be the sample space.

Then, n(S) = 52C2 =	(52 x 51)	= 1326.
	(2 x 1)

Let E = event of getting 1 spade and 1 heart.

n(E)	= number of ways of choosing 1 spade out of 13 and 1 heart out of 13
	= (13C1 x 13C1)
	= (13 x 13)
	= 169.

P(E) =	n(E)	=	169	=	13	.
	n(S)		1326		102

Let the ten's digit be x and unit's digit be y.

Then, (10x + y) - (10y + x) = 36

9(x - y) = 36

x - y = 4.

Video Explanation: https://youtu.be/7QOJjAmGVx0

Let the number be x.

Then, x + 17 =	60
	x

x² + 17x - 60 = 0

(x + 20)(x - 3) = 0

x = 3.

Let the required number of bottles be x.

More weavers, More mats (Direct Proportion)

More days, More mats (Direct Proportion)

Wavers	4	:	8		:: 4 : x
Days	4	:	8

4 x 4 x x = 8 x 8 x 4

x =	(8 x 8 x 4)
	(4 x 4)

x = 16.

Let the man's rate upstream be x kmph and that downstream be y kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

		x x 8	4		= (y x 4)
			5

	44	x =4y
	5

y =	11	x.
	5

Required ratio =		y + x		:		y - x
		2				2

=		16x	x	1		:		6x	x	1
		5		2				5		2

=	8	:	3
	5		5

   = 8 : 3.

At 5 o'clock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

40 min. spaces are gained in		60	x 40	min	=	43	7	min.
		55					11

Required time = 43	7	min. past 5.
	11

Let original length = x and original breadth = y.

Original area = xy.

New length =	x	.
	2

New breadth = 3y.

New area =		x	x 3y		=	3	xy.
		2				2

Increase % =		1	xy x	1	x 100	%	= 50%.
		2		xy

Clearly, I only gives the answer.

Similarly, II only gives the answer.

And, III only gives the answer.

Correct answer is (D).

Let the tens and units digit be x and y respectively.

  I. (10x + y) - (10y + x)       x - y = 3.

 II. x - y = 3.

III. x - y = 3.

Thus, even all the given three statements together do not give the answer.

Correct answer is (E).

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

Required number of numbers = (1 x 5 x 4) = 20.

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
	= 7 x 6 x 5 x 6 x 5 + (7C3 x 6C1) + (7C2) 3 x 2 x 1 2 x 1
	= 525 + 7 x 6 x 5 x 6 + 7 x 6 3 x 2 x 1 2 x 1
	= (525 + 210 + 21)
	= 756.

Each number is double the preceding one plus 1.

So, the next number is (255 x 2) + 1 = 511.

Let investment in 12% stock be Rs. x.

Then, investment in 15% stock = Rs. (12000 - x).

	12	x x +	15	x (12000 - x) = 1360.
	120		125

	x	+	3	(12000 - x) = 1360.
	10		25

5x + 72000 - 6x = 1360 x 50

x = 4000.