The total number of people, who visited the zoo on all three days of the week is 10000

On Monday 1000 children visited the zoo 

The ratio of children, who visited the zoo on Monday and Wednesday is 2 : 1 respectively.

Then 2 unit = 1000 

⇒ 1 unit = 500 hence 500 children visited the zoo on Wednesday.

The total number of children, who visited the zoo on all three days is 2500

Then, the number of children, who visited the zoo on Tuesday = 2500 -(1000+500)

⇒ 2500 - 1500 = 1000

The number of men, who visited the zoo on Tuesday is 50% more than the number of children, who visited the zoo on Wednesday 

⇒ 500 × 150/ 100 = 750

2000 women visited on Wednesday 

Men, who visited the zoo on Monday and women, who visited the zoo on Wednesday are 5 : 4 respectively.

Then 4 unit = 2000 so 5 unit = 2500

The number of men visited on Monday is 2500

The Total number of men, who visited on all three days is 70% more than the total number of children, who visited on all three days

⇒ 2500 × 170 / 100

⇒ 4250

Then, the number of men visited on Wednesday is =  4250- (2500+750)

⇒ 4250 - 3250 = 1000

The number of men, who visited the zoo on Wednesday is 500 more than the number of women, who visited the zoo on Monday.

⇒ 1000 - 500 = 500

Total number of women visited on all three days 

⇒ 10000 -(4250+2500) = 3250

Then, the number of women, who visited on Tuesday 

⇒ 3250-(2000+500) = 750

The number of children, who visited on Wednesday are 500 

The number of men, who visited on Monday are 2500

As the number of men, who visited on Monday is more than the number of children, who visited on Wednesday, so

Then 2500 - 500 = 2000

⇒ (2000 / 2500 ) × 100

⇒ ( 4 / 5) × 100

⇒ 80% 

Hence, 80%, Less is the correct answer.

Let the total marks and passing marks of the examination be x and y respectively

∴ Marks obtained by Kashyap 

⇒ (70/100) × x = y + 150 ----(i)

Marks obtained by Sunaina 

⇒ (60/100) × x = y + 100 ----(ii)

Subtracting (ii) from (i)

⇒ {(70/100) × x} – {(60/100) × x} = y + 150 – y – 100

⇒ (10/100) × x = 50

⇒ x = 500

Putting value of x in (ii)

(60/100) × 500 = y + 100

⇒ 300 = y + 100

⇒ y = 200

∴ Passing percentage of the examination = (200/500) × 100 = 40%

Given:

A’s age = 1/4 (Mother’s age two years ago)

Mother’s age = 2 × (B’s age after 10 years)

B’s 12^th birthday was 4 years ago

Concept:

4 years ago B’s age was 12. So present age of B is 16

Explanation:

Let’s denote A’s mother’s age by M

⇒ A = 1/4 × (M – 2)

And, M + 10 = 2 × (B + 10)

B = 16 (∵ 4 years ago B’s age was 12)

Calculation:

According to the Question,

 M + 10 = 2 × (16 + 10)

⇒ M = 42

We have, A = 1/4 (M – 2)

⇒ A = 1/4 × (42 – 2) = 10

∴ Present age of A is 10 years

Given:

A container contains 6 white, 8 blue and 4 red marbles. Three marbles are drawn at random from the container

Concept used:

The classical definition of probability

Formula used:

Probability = Favorable Outcome / Total Outcome

P(E) = n(E)/n(S)

ⁿC_r = n! / r!(n - r)!

ⁿC_r = ⁿC_{(n - r)}

Calculation:

Total number of marbles is 6 + 8 + 4 = 18

Let S be the sample space

n(S) = Total number of ways of drawing 3 marbles out of 18 = ¹⁸C₃

Let E = Event of drawing 3 marbles, all of them are blue

n(E) = Number of ways of drawing 3 marbles, all of them are blue

Number of ways of drawing 3 marbles from the total 8 = ⁸C₃

P(E) = n(E) / n(S)

⇒ ⁸C₃/¹⁸C₃

⇒ {(8 × 7 × 6)/(1 × 2 × 3)}/{(18 × 17 × 16)/(1 × 2 × 3)}

⇒ 56/816

⇒ 7/102

∴ The probability that all of them are blue is 7/102.

Given:

Rate of interest = 30% per annum

Principal = 4600 Rs.

Calculation:

Let the installment paid in compound interest by 'X' is 'A' Rs.

⇒ 4600 = A/[1 + (3/10)] + A/[1 + (3/10)2]

⇒ 4600 = A × [(10/13) + (10/13)2]

⇒ 4600 = A × (230/169)

⇒ A = 3380 Rs.

Amount paid = 3380 + 3380 = 6760 Rs.

Let the installment paid in simple interest by 'X' is 'B' Rs.

Simple interest installment = 100 × (Amount)/[100 × n + n × (n - 1) × (r/2)] 

⇒  100 × (Amount) = Simple interest installment × [100 × n + n × (n - 1) × (r/2)]

⇒ 100 × [Principal + Interest] = B × [100 × n + n × (n - 1) × (r/2)]

⇒ 100 × [Principal + (Principal × Rate × time)/100] = B × [100 × n + n × (n - 1) × (r/2)]

⇒ 100 × [Principal(100 + Rate × time)/100] = B × [100 × n + n × (n - 1) × (r/2)]

⇒ 100 × 4600 × [(100 + 2 × 30)/100] = B × [100 × 2 + 2 × 1 × (30/2)]

⇒ 4600 × 160 = B × 230

⇒ B = 3200

Amount paid = 3200 + 3200 = 6400 Rs.

Required difference = 6760 - 6400 = 360 Rs.

Hence, the correct answer is Rs. 360

Total quantity of mixture( Milk + Water)  in vessel = 180

Quantity of milk in the vessel = 180/9 ×  5 = 100

Quantity of water in the vessel = (180 - 100) = 80

Now the quantity of mixture removed = x

Quantity of milk removed from the mixture = (x × 5/9) = 5x/9

Quantity of water from the mixture = (x × 4/9) = 4x/9

[(100 - 5x/9)/(80 - 4x/9 + x/3)] = 1/1

Multiply equation by 9

 9 ×  (100 - 5x/9) = 9 ×  (80 - 4x/9 + x/3)

900 - 5x = 720 - 4x + 3x

900 - 5x = 720 - x

900 = 720 = 4x

4x = 180

x = 45

Now the quantity of milk in vessel = (100 - 45 ×  5/9) = 75 litres

Quantity of water in the vessel = (80 - 45 ×  4/9) = 60 + 45/3 = 75 litres

Now y litres of milk is added then the milk to water in the final mixture is 7: 5.

(75 + y)/(75) = 7/5

(375 + 5y) = 525

5y = 150

y = 30

Find  (x + y) = (45 + 30) = 75

Let, the speed of bike = 's' km/hr

A bike travels 'x' km in 1 hour and 15 minutes

x/s = 1 hour and 15 minutes

x/s = 1.25

x = 1.25s ....(1)

The same bike travels 48 km more, then it will take 0.75 hours more

(x + 48)/s = (1.25 +0.75)

x + 48 = 2s....(2)

Substitute equation (1) in (2)

1.25s + 48 = 2s

0.75s = 48

s = 64 km/hr

Distance traveled in 4 hours 42 min = 64 × 4.7 = 300.8 km

A train can cross an electric pole in 40 seconds and bridge of length 170m in 50 seconds. 

let the length of train be x and speed of train be y.

hence x / y = 40

x = 40y.

(170 + x) / y = 50

(170 + 40y) / y = 50

170 + 40y = 50y

y = 17.

hence x / 17 = 40

x = 680m.

hence the speed of train is 17 m/s and length of train is 680m.

time taken by (in sec) train to cross a man running at 46.8 kmph in same direction as that of train

speed of a man in m/s = 46.8 ×  5 / 18 = 13 m/s.

hence speed in same direction = 17 – 13 =4 m/s.

hence distance / speed = time

680 / 4 = 170 seconds.

Given:

Ratio of radius of a circle and side of a square = 2:3

Breadth of the rectangle = Side of square

Length of the rectangle= 10/7^th× Breadth of the rectangle

Perimeter of the rectangle= 102 cm

Formula Used:

Perimeter of square = 4 × Side

Perimeter of rectangle = 2(length + breadth)

Area of square = side²

Area of rectangle = length × breadth

Calculation:

Suppose the length of the rectangle and breadth of the rectangle is 10x and 7x, respectively.

⇒ 2(10x + 7x) = 102

⇒ 17x = 51

⇒ x = 3

Length of the rectangle = 30 cm

Breadth of the rectangle = 21 cm

∴ Side of the square = 21 cm

The ratio of the radius of a circle and the side of a square is 2: 3

⇒ 3 units = 21

⇒ 1 unit = 7

⇒ 2 unit = 14 cm

The radius of the circle is 14 cm

So, the area of the circle = π(14)²

⇒ 22/7 × 14 × 14

⇒ 616 sq. cm

Calculation:

Let the MP of a laptop be Rs. 100a

At a discount of (p + 5)%, SP = 100a × (100 - p - 5)%

100a × (95 - p)/100 = (95 - p)a

At an additional discount of 10%, SP = (95 - p)a × (100 - 10)/100

(95 - p)a × 90/100 = 7560

(95 - p)a × 9/10 = 7560  

(95 - p)a = 8400      ......(1)

When overall discount is 3p%, SP = 100a × (100 - 3p)/100

(100 - 3p)a   ......(2)

Since SP are equal

(95 - p)a × 9/10 = (100 - 3p)a 

855 - 9p = 1000 - 30p

21p = 145

p = 145/21

Put the value of p in eq(1), we get

(95 - 145/21)a = 8400  

a = 95.35

Marked Price of the laptop = 100 × 95.35 = Rs. 9535