Jun 20, 2018

Ratio and proportion are one of those concepts that may pop up in about any GRE numerical problem. You may have to calculate the ratio between 2 angles forming intersecting lines, or you may have to calculate the ratio of speeds a person drove at.

With such broad applications, it’s imperative for you to know about these concepts in minute details. Here, in this post, we have come up with a few sample problems for your practice. If you are a serious GRE aspirant, consider going through them all without any further ado.

**Q1. A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.**

**A) 360, 160, 200 **

**B) 160, 360, 200**

**C) 200, 360,160 **

**D) 200,160,300**

Answer: C) 200, 360,160

*Solution:*

Let the no. of coins be 5x ,9x , 4x respectively

Now given total amount = Rs.206

Therefore, (.50)(5x) + (.25)(9x) + (.10)(4x) = 206

Solving the equation, we get x = 40

=> No. of 50p coins = 200

=> No. of 25p coins = 360

=> No. of 10p coins = 160

**Q2. A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.**

**A) 10 **

**B) 12**

**C) 15 **

**D) 18**

Answer: A) 10

*Solution:*

Let the quantity of alcohol and water be 4x litres and 3x litres respectively

4x/(3x+5) = 4/5

or, 20x = 4(3x+5)

or, 8x = 20

or, x = 2.5

Quantity of alcohol = (4 x 2.5) litres = 10 litres.

**Q3. If Rs. 782 be divided into three parts, proportional to 12:23:34, then the first part is?**

**A) Rs. 182 **

**B) Rs. 190**

**C) Rs. 192 **

**D) Rs. 204**

Answer: D) Rs. 204

*Solution:*

Rs.(782*6/23)

Given ratio = 1/2 : 2/3 : 3/4 = 6 : 8 : 9

1st part = Rs.(782* 6/23) = Rs. 204

**Q4. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?**

**A) 2 : 3 : 4**

**B) 6 : 7 : 8**

**C) 6 : 8 : 9**

**D) None of these**

Answer: A) 2 : 3 : 4

*Solution:*

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

or, (140/100 x 5x) , (150/100 x 7x) and (175/100 x 8x)

or, 7x, 21x/2 and 14x

Therefore, the required ratio = 7x : 21x/2 : 14x

or, 14x : 21x : 28x

or, 2 : 3 : 4

**Q5. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:**

**A) 20 litres**

**B) 30 litres**

**C) 40 litres**

**D) 60 litres**

Answer: D) 60 litres

*Solution:*

Quantity of milk = (60 x 2/3) litres = 40 litres.

Quantity of water in it = (60 - 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

Then, milk : water = (40/20+x).

Now, (40/20+x) = 1/2

or, 20 + x = 80

or, x = 60

Therefore, quantity of water to be added = 60 litres.

**Q6. The ratio of Alice's pay to Bob's pay is 5:4. The ratio of Bob's pay to Charlie's pay is 10:9. If Alice is paid $75, how much is Charlie paid?**

**A) $55**

**B) $57**

**C) $54**

**D) $40**

Answer: C) $54

*Solution:*

Since the ratio of Alice's pay to Bob's pay is , Bob's pay must be b, where 5/4 = 75/b.

Cross-multiplying the denominators, we get , 5b = 4 (75); so b = 60.

Continuing in the same way, we compare Bob to Charlie:

10/9 = 60/c

or, 10c = 9 (60)

or, c = 54

Thus, Charlie is paid $54.

All the best for your GRE examination!

Article Posted in: Exam Preparation