Mock Test 3 Arithmetic Questions with Explanations

Mock Test 3 Arithmetic Questions with Explanations

1. If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5 ?

Explanation:

3√5 + √125 = 17.88

3√5 + √25 x 5 = 17.88

3√5 + 5√5 = 17.88

8√5 = 17.88

√5 = 2.235

√80 + 6√5 = √16 x 5 + 6√5

= 4√5 + 6√5

= 10√5 = (10 x 2.235) = 22.35

2.       A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

Explanation:

Let number of notes of each denomination be x.

Then x + 5x + 10x = 480

16x = 480

x = 30.

Hence, total number of notes = 3x = 90.

3. It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

Explanation:

Let 2³² = x. Then, (2³² + 1) = (x + 1).

Let (x + 1) be completely divisible by the natural number N. Then,

(2⁹⁶ + 1) = [(2³²)³ + 1] = (x³ + 1) = (x + 1)(x² – x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

4.       A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 – 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes		3	x 60		= 90 days.
		2

So, A takes 30 days to do the work.

A’s 1 day’s work =	1
	30

 

B’s 1 day’s work =	1
	90

 

(A + B)’s 1 day’s work =		1	+	1		=	4	=	2
		30		90			90		45

 

A and B together can do the work in	45	= 22	1	days.
	2		2

 

5.        If selling price is doubled, the profit triples. Find the profit percent.

Explanation:

Let C.P. be Rs. x and S.P. be Rs. y.

Then, 3(y – x) = (2y – x)    y = 2x.

Profit = Rs. (y – x) = Rs. (2x – x) = Rs. x.

Profit % =		x	x 100	% = 100%
		x

6. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R =		100 x 60		= 10% p.a.
		100 x 6

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I.	= Rs. 12000 x 1 + 10 3 – 1 100
	= Rs. 12000 x 331 1000
	= 3972.

7. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

Explanation:

Perimeter = Distance covered in 8 min. =		12000	x 8	m = 1600 m.
		60

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) m² = 153600 m².