Quants

 Directions (1-5): Study the following pie-charts and answer the questions that follow: There are 5 sections in a class with given information in the pie-char

1. Find the ratio of the total number of students in sections C and D to number of males in the same sections. 

Explanation:

 Students in C and D = (15+13)/100 * 2400 = 672

 No of males in C and D = (6+20)/100 * 1300 = 338

 So ratio = 672 : 338 = 336 : 169What is the average number of females in sections A and C?

Explanation: 

Students in A and C = (37+15)/100 * 2400 = 1248 

No of males in A and C = (33+6)/100 * 1300 = 507 

So females in A and C = 1248 – 507 = 741, 

so average = 741/2 = 370.5

Find the angle subtended by C section in the total number of students diagram.

Explanation: 

15/100 * 360 = 54o

Find the ratio of the number of males in D section to the females in section E.

Explanation:

 Males in D = 20/100 * 1300 = 260 

Students in E = 10/100 * 2400 = 240, 

males in E = 17/100 * 1300 = 221, 

so females in E = 240 – 221 = 19 

Ratio = 260 : 19

What is the number of females in sections A and B? 

Explanation:

 Students in A and B = (37+25)/100 * 2400 = 1488 

Males in A and B = (33+24)/100 * 1300 = 741 

So females = 1488 – 741 = 747

A bag contains 3 white balls, 5 black balls and 4 yellow balls. 3 balls are drawn at random. What is the probability that atmost 1 ball is black in color?

Explanation: 

Atmost 1 black means 0 black or 1 black 

Case 1 : none is black None is black means 3 balls from 7 balls (3 w + 4 y), ways are 7C3 = 7*6*5/3*2*1 = 35 

Case 2: 1 ball black and other 2 white or yellow Ways are 5C1 × 7C2 = 5 * 7*6/2*1 = 105 

There are a total of 12 balls. Ways for drawing 3 balls is 12C3 = 12*11*10/3*2*1 = 220

 So required prob. = 35+105/220 = 140/220 = 7/11

A man reaches at 10 AM from P to Q when his average speed is 15 km/hr and reaches at 12 noon when the average speed is 10 km/hr. What should be the average speed to reach at 9 AM?

Explanation:

 Let distance from P to Q is ‘d’ and time taken to reach at 9 AM is ‘t’ 

Then with 10 AM, time becomes ‘t+1’, so d/(t+1) = 15 

With 12 noon, time becomes ‘t+3’, so d/(t+3) = 10 

Solve the equations, t = 3 hrs, d = 60 km 

So speed to reach at 9 AM = 60/3 = 20 km/hr

or shortcut use logic

A and B started a business by investing Rs 6400 and Rs 4600 respectively. After 4 months both withdraw Rs 400 and C joined them with Rs 8000. At the end of year, what will be the ratio of their profits?

Explanation: 

A’s share : B’s share : C’s share 6400*4 + 6000*8 : 4600*4 + 4200*8 : 8000*8 Two 0’s get cancelled, we are left with 64*4 + 60*8 : 46*4 + 42*8 : 80*8 

We can see that 8 gets cancelled from each term, now left with 32 + 60 : 23 + 42 : 80

92 : 65 : 80

A’s age 8 years ago was four less than B’s age that time. Ratio of A’s age 8 years after and B’s age that time will be 6 : 7. Find the ratio of A’s age after 4 years to that of B’s age at that time.

Explanation: 

Let the present ages of A and B are x and y respectively. 8 years ago, x-8 = (y-8) – 4. This gives x – y = -4 

After 8 years, x+8/ y+8 = 6/7.This gives 7x – 6y = -8 

Solve both equations, x = 16, y = 20 

So required ratio = (16+4) : (20+4) = 20 : 24 = 5 : 6

A mixture contains A and B in the ratio of 5 : 3. 16 litres of this mixture is taken out and 5 litres of A is poured in. the new mixture has ratio of A to b as 11 : 6. Find the total original quantity of mixture.

Explanation: 

A = 5x, B = 3x After taking out 16 l of mixture, A = 5x – 5(5+3) * 16 = 5x – 10 B = 3x – 3(5+3) * 16 = 3x – 6 

After pouring 5 l of A, A = 5x – 10 + 5 = 5x – 5 

So now, 5x-5/3x-6 = 11/6 Solve, x = 12

 Total original quantity = 5x+3x = 8x = 8*12 = 96 litres