Mock Test 1 Arithmetic Answers with Explanations

Mock Test 1 Arithmetic Answers with Explanations

1. The largest 4 digit number exactly divisible by 88 is:

2. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

	27x + 17y	= 23
	x+ y

27x + 17y = 23x + 23y

4x = 6y

	x	=	3	.
	y		2

 

3. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

Explanation:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 – x).

		20 – x	x 100 = 25
		x

2000 – 100x = 25x

125x = 2000

x = 16.

4. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Explanation:

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.

5. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

Explanation:

After 10 days : 150 men had food for 35 days.

Suppose 125 men had food for x days.

Now, Less men, More days (Indirect Proportion)

125 : 150 :: 35 : x       125 x x = 150 x 35

x =	150 x 35
	125

x = 42.

6. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

Explanation:

Let speed of the car be x kmph.

Then, speed of the train =	150	x	=		3	x	kmph.
	100				2

 

	75	–	75	=	125
	x		(3/2)x		10 x 60

 

	75	–	50	=	5
	x		x		24

 

x =		25 x24		= 120 kmph.
		5

 

7. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

Explanation:

Let original length = x metres and original breadth = y metres.

Original area = (xy) m².

New length =		120	x	m	=		6	x	m.
		100					5

 

New breadth =		120	y	m	=		6	y	m.
		100					5

 

New Area =		6	x x	6	y	m2	=		36	xy	m2.
		5		5					25

The difference between the original area = xy and new-area 36/25 xy is

= (36/25)xy – xy

= xy(36/25 – 1)

= xy(11/25) or (11/25)xy

Increase % =		11	xy x	1	x 100	%	= 44%.
		25		xy

 

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