[Download PDF] TS Police SI Mains 2018 Arithmetic and Reasoning Paper with Solutions

Instructions

For the following questions answer them individually

Question 91

The cost of a fencing around a circular field at the rate of Rs. 45 per meter is Rs. 15,840. Then the area of the field, in square meters, is (Take $$\pi = \frac{22}{7}$$)

Video Solution

Solution

Circumference of the field = 15840/45 = 352 meters
Also, 2*(22/7)*R = 352
R = 56 meters

Area of the field = (22/7)*56*56 = 9856 sq. meters

Question 92

A wheel makes 60 revolutions in covering a distance of 990 meters. The radius of the wheel, in meters, is (Take $$\pi = \frac{22}{7}$$)

Video Solution

Solution

60*2*(22/7)*R = 990
R = 2.625 meters

Question 93

The volume of a cube in cubic feet whose total surface area is 486 square feet, is

Video Solution

Solution

6*Side*Side = 486
Side = 9 feet

Volume = 9*9*9 = 729 cubic feet

Question 94

By what percentage should the radius of a sphere be increased so that the volume increases by 200%?

Video Solution

Solution

Volume increases by 200% means the volume must becomes 3 times the original one
Hence, V2 = 3*V1
(4/3)*(22/7)*(R2)*(R2)*(R2) = 3*(4/3)*(22/7)*(R1)*(R1)*(R1)
R2 = $$\sqrt[\ 3]{3}$$ * R1

Hence, percentage increase = ({[$$\sqrt[\ 3]{3}$$ * R1] - R1}/R1)*100 = $$\left(\sqrt[\ 3]{3}-\ 1\right)\cdot100$$

Question 95

The length and breadth of a rectangle are 100 cms. and 60 cms. If the length increases by 5% and the breadth decreases by 4%, then, the error percentage in the area calculated from these measurements is

Video Solution

Solution

Length tabulated would be 105 cm and breadth considered = 0.96*60 = 57.6 cm
Area calculated = 105*57.6 = 6048 sq. cm
Actual area = 6000 sq. cm

error = (48/6000)*100% = 0.8%

Question 96

The sum of all two digit numbers which leave remainder 4 when divided by 11 is

Video Solution

Solution

It would be sum of numbers from (11*1)+4 to (11*8)+4

Adding them up, we get: (4*8)+11*(1+2+3+4+5+6+7+8) = 32 + 11*36 = 428

Question 97

If in a leap year, January $$8^{th}$$ is a Sunday, the day on August $$15^{th}$$ in the same year is

Video Solution

Solution

January 1 will also be a Sunday.
August 15 is 227 days from January 1.

227/7 ==> R = 3
Move 3 days from Sunday: Monday, Tuesday, Wednesday.

Question 98

If A earns 50% more than B and B earns x % less than A then x =

Video Solution

Solution

Let B earn Rs. 100. Hence, A earns Rs. 150
Hence, earning of B with respect to A = (100/150)*100% = (200/3)% i.e. 66.67%

Hence, B earns 33.33% less than A.

Question 99

The largest positive integer k such that $$12^k$$ divides $$(109)!$$ is

Video Solution

Question 100

The number of positive integral divisors of 37800 is

Video Solution

Solution

$$37800=2^3\cdot3^3\cdot5^2\cdot7$$

Hence, number of factors of 37800 = (3+1)*(3+1)*(2+1)*(1+1) = 96

CAT Content

TS Police SI Mains 2018 Arithmetic and Reasoning

The cost of a fencing around a circular field at the rate of Rs. 45 per meter is Rs. 15,840. Then the area of the field, in square meters, is (Take $$\pi = \frac{22}{7}$$)

A wheel makes 60 revolutions in covering a distance of 990 meters. The radius of the wheel, in meters, is (Take $$\pi = \frac{22}{7}$$)

The volume of a cube in cubic feet whose total surface area is 486 square feet, is

By what percentage should the radius of a sphere be increased so that the volume increases by 200%?

The length and breadth of a rectangle are 100 cms. and 60 cms. If the length increases by 5% and the breadth decreases by 4%, then, the error percentage in the area calculated from these measurements is

The sum of all two digit numbers which leave remainder 4 when divided by 11 is

If in a leap year, January $$8^{th}$$ is a Sunday, the day on August $$15^{th}$$ in the same year is

If A earns 50% more than B and B earns x % less than A then x =

The largest positive integer k such that $$12^k$$ divides $$(109)!$$ is

The number of positive integral divisors of 37800 is

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