Ration and Proportion Problems for Bank PO Mains | Download PDF

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1) In a company, there are 80 IT employees, 60 HR employees, 100 Marketing employees and 40 Sales employees. Ratio of the number of male to female IT employees in a company is 3:1 and the ratio of the number of male to female HR employees in a company is 2:1. If the male employees of marketing department is 20 more than that of the number of female employees in marketing department and the half of the employees in sales department are male, then what is the ratio of the total number of male to female employees from a company?

A.3:2

B.5:3

C.8:5

D.9:5

E.None of these


2) Ratio of the cost price of mobile to laptop is 1: 3 and then Ram purchased x number of laptops and 6 mobiles, while Rahul purchased 6 laptops and x mobiles. If the total amount paid by Rahul is 40% more than that of the total amount paid by Ram, then find the value of x?

A.4

B.2

C.3

D.8

E.6


3) If the ratio of the number of balls in box A and box B is 4:5 and the ratio of the balls in box C to D is 3: 4. If the number of balls in box D is 4 less than the number of balls in B and the average number of balls in all the boxes together is 87, then what is the number of balls in box A?

A.100

B.60

C.40

D.80

E.None of these


4) If the number of female employees in company A is 50% more than the number of male employees in the same company and the number of female employees in company B is twice the number of male employees in the same company. If the total number of employees in A is 120 more than the number of employees in B, then what is the ratio of the number of male to female employees in A and B together?

A.3:2

B.2:3

C.4:5

D.Cannot be determined

E.None of these


5) The ratio of the number of male to female in Chennai and Bangalore is 3:2 and 7:3 respectively. If 20% of the male from Chennai are undergraduate and 60% female from Bangalore are postgraduate. If the postgraduate males from Chennai and postgraduate female from Bangalore is 3300 and the total number of people in Chennai and Bangalore is equal, then what is the total male population in Chennai and Female population in Bangalore?

A.4500

B.4200

C.4000

D.4800

E.None of these


6) There are three boxes A, B and C and each of them contains two different color balls red and yellow. If the ratio of the total number of balls from A, B and C is 2: 3: 1 and then one – fifth of the balls from C is red, two-fifth of the balls from B is red and half of the balls from A is red, then the number of yellow balls from all the boxes together is what percent of the total number of balls from all the boxes together?

A.40%

B.50%

C.60%

D.Cannot be determined

E.None of these


7) Ratio of the number of boys to girls in class A is 4: 5 and the ratio of the boys to girls in class B is 4: 3. If 10 girls left from class A and 10 boys left from class B, then the number of students from class A and B is equal. What is the ratio of the total number of students from class A to B?

A.3: 4

B.5: 3

C.5: 8

D.4: 7

E.None of these


8) Ratio of the monthly income of A to B is 4:3 and the ratio of the monthly income of B to C is 2:1. If the difference between the C’s monthly income and his savings is Rs.12000 and the saving’s of C is half of his expenditure, then what is the average of the income of A, B and C?

A.Rs.34000

B.Rs.31000

C.Rs.27000

D.Rs.29000

E.None of these


9) Atul divides some money among his three children A, B and C. The ratio of amount received by A and C together to the amount received by B is 5:2. C received 150% of the amount received by A. If the amount received by C is Rs. 1500. Find the sum of amount received by A and B together. 

A.Rs. 1500

B.Rs. 1000

C.Rs. 2000

D.Rs. 2500

E.Rs. 3000


10) Ratio of the employees in company A to B is 6: 5 and the number of employees in C to A is 13: 10. If the ratio of the number of male to female employees in A, B and C is 7: 5, 2: 3 and 7: 6 respectively, then the number of female employees in all the companies together is approximately what percent of the total number of employees in all the companies together?

A.42%

B.45%

C.48%

D.51%

E.54%

 

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Answers :

1) Answer: D

Male IT employees = 80 * ¾ = 60

Female IT employees = 80 * ¼ = 20

Male HR employees = 2/3 * 60 = 40

Female HR employees = 1/3 * 60 = 20

Male employees in marketing = 40 + 20 = 60

Female employees in marketing = 40

Male employees in sales = 40/2 = 20

Female employees in sales = 40/2 = 20

Required ratio = (60 + 40 + 60 + 20):(20 + 20 + 40 + 20)

= 180:100

=9:5


2) Answer: C

CP of mobile = y

CP of laptop =3y

Total amount paid by Ram =(x*3y)+(6 * y) = 3xy + 6y

Total amount paid by Rahul = (6 * 3y) + (x * y) = 18y + xy

Amount Difference= (18y+xy) – (3xy + 6y)

= 12y – 2xy

(12y-2xy) = (40/100)(3xy+6y)

60y – 10xy = 6xy + 12y

48y = 16xy

x = 3


3) Answer: D

Number of balls in A = 4x

Number of balls in B = 5x

Number of balls in D = 5x – 4

Number of balls in C = ¾ * (5x – 4)

(4x + 5x + 5x – 4 + (15x – 12)/4)/4 = 87

14x + 15x/4 = 87 * 4 + 7

71x = 1420

x = 20

Number of balls in A = 20 * 4 = 80


4) Answer: D

Number of male employees in A = x

Number of female employees in A = x * 150/100 = 3x/2

Total number of employees in A = x + 3x/2 = 5x/2

Number of male employees in B = y

Number of female employees in B = 2y

Total number of employees in B = 3y

5x/2 – 3y = 120

5x – 6y = 240

5x = 240 + 6y

We cannot find the answer.


5) Answer: A

Number of male in Chennai = 3x

Number of female in Chennai = 2x

Number of male in Bangalore = 7y

Number of female in Bangalore = 3y

Number of population is equal in Chennai and Bangalore

3x + 2x = 7y + 3y

x = 2y

Number of postgraduate male in Chennai = 80/100 * 3x = 2.4x

Number of postgraduate female in Bangalore = 60/100 * 3y = 1.8y

2.4x + 1.8 * (x/2) = 3300

4.8x + 1.8x = 6600

x = 1000

Male population in Chennai and Female population in Bangalore = 3x + 3y = 3x + (3 * x/2)

= 4.5x

Required total = 4.5 * 1000 = 4500


6) Answer: C

Yellow balls from A = 1/2 * 2x = x

Yellow balls from B = 3/5 * 3x = 9x/5

Yellow balls from C = 4/5 * x = 4x/5

Total yellow balls = x + 9x/5 + 4x/5 = 18x/5

Required percentage = (18x/5)/6x * 100 = 60%


7) Answer: E

Number of boys in class A = 4x

Number of girls in class A = 5x

Number of boys in class B = 4y

Number of girls in class B = 3y

5x + 4x – 10 = 4y – 10 + 3y

9x = 7y

x/y = 7/9


8) Answer: A

C’s income = x

Expenditure = y

Savings = s

x = y + s

y + s – s = 12000

y = 12000

Savings = 12000 * ½ = 6000

x = 12000 + 6000 = 18000

B’s income = 2/1 * 18000 = 36000

A’s income = 4/3 * 36000 = 48000

Average income of A, B and C = (48000 + 36000 + 18000)/3 = 34000


9) Answer: C

Let the total amount divided by 70x

Amount received by A and C together = 70x*(5/7) = 50x

And amount received by B = 70x*(2/7) = 20x

Let the amount received by A = 10k and amount received by C will be 150% of 10k = (150/100)*10k = 15k

Amount received by A and C together = 10k + 15k = 25k

Since 50x = 25k

2x = k

Amount received by A = 10k = 10*2x = 20x

Amount received by C =15k = 1500

k =100

2x = 100

x = 100/2 = 50

Therefore, the sum of amount received by A and B = 20x+20x = 40x = 40*50 = Rs. 2000


10) Answer: C

Number of employees in A:B:C= 30: 25: 39

Number of female employees in A = 30x * 5/12 = 12.5x

Number of female employees in B = 3/5 * 25x = 15x

Number of female employees in C = 39x * 6/13 = 18x

Required percentage = (12.5x + 15x + 18x)/94x * 100

= 45.5x/94x * 100

= 48%

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