A farmer has cows and buffaloes in the ratio 3:1. If he buys 10 more cows and 2 more buffaloes, the given ratio becomes 4:1. What is the current number of cows?

a)
3

b)
6

c)
9

d)
12

e)
15

Correct answer is option 'B'. Can you explain this answer?

Question

A farmer has cows and buffaloes in the ratio 3:1. If he buys 10 more cows and 2 more buffaloes, the given ratio becomes 4:1. What is the current number of cows?

a)
3
b)
6
c)
9
d)
12
e)
15

Correct answer is option 'B'. Can you explain this answer?

Answer

Let's assume that the current ratio of cows to buffaloes is 3x:1x, where x is a constant.

According to the given information, if the farmer buys 10 more cows and 2 more buffaloes, the ratio becomes 4:1.

So, the new ratio of cows to buffaloes is (3x+10):(1x+2) = 4:1

Cross-multiplying, we get:

4(1x+2) = 3x+10

Simplifying:

4x+8 = 3x+10

x = 2

Therefore, the current ratio of cows to buffaloes is 3x:1x = 6:2 or 3:1

To find the current number of cows, we can use the ratio:

Let the current number of cows be 3y and the current number of buffaloes be y.

Then, 3y+10: y+2 = 4:1

Cross-multiplying, we get:

4( y+2) = 3y+10

Simplifying:

y = 4

Therefore, the current number of cows is 3y = 3(4) = 12.

Hence, the correct option is (b) 12.

Answer

Answer

X - first ratio variable
y - second ratio variable

3x + 10 = 4y
X + 2 = y
....
X = y - 2
3(y-2) +10 = 4y
3y - 6 +10 = 4y
+4 = 4y - 3y
If y = 4,
X = y-2 = 4-2 = 2
Total number of cows no = 3x = 3*2 = 6 (Option B)

Answer

D

Similar GMAT Doubts

The ratio of a two digit number to a number formed by reversing its digits is 4:7. Which of the following is the sum of all the numbers of all such pairs?

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2025

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

Top Courses for GMAT

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams