Question

If 21 cows eat as much as 15 buffaloes, how many cows will eat as much as 35 buffaloes?
(a) 49
(b) 56
(c) 45
(d) None of these

Answer 1

Hint: First, we will assume cow to some variable ‘c’ and buffalo to ‘b’. Then we will find 1 cow is equal to how many buffaloes. So, we get as \[c=\dfrac{5}{7}b\] . Using this, we will apply unitary method 1 cow is equal to \[\dfrac{5}{7}\] buffaloes then how many cows equal to 35 buffaloes. Thus, on solving, we will get the answer.

Complete step-by-step answer:
Here, we will assume cows to be let say some variable ‘c’ and buffaloes to be ‘b’.
Now, we are told that 21 cows eat as much as 15 buffaloes so, we can write it as
\[21c=15b\]
So, dividing both side by 21, we get value of ‘c’ as
\[c=\dfrac{15}{21}b\]
On further simplifying, we get as
\[c=\dfrac{5}{7}b\] ………………………….(1)
Now, we have to find how many cows will be equal to 35 buffaloes. So, using a unitary method we can say that if 1 cow is equal to \[\dfrac{5}{7}\] buffaloes (from equation (1)), then how many cows equal to 35 buffaloes.
In mathematical form, we can write it as
\[\begin{align}
  & 1c=\dfrac{5}{7}b \\
 & ?=35b \\
\end{align}\]
On further solving, we get as
\[=\dfrac{35\times 1}{\dfrac{5}{7}}\]
Now, denominator 7 will go in numerator and we get as
\[=\dfrac{35\times 1\times 7}{5}=\dfrac{245}{5}\]
\[c=49\]
Thus, 49 cows will eat as much as 35 buffaloes.
So, the correct answer is “Option A”.

Note: Another approach of solving is directly by doing unitary method i.e. 21cows equal to 15buffaloes then how many cows equal to 35buffaloes. We get as
\[\begin{align}
  & 21c=15b \\
 & ?=35b \\
\end{align}\] . On solving this we will get the same answer i.e. 49 cows. Also, we can find an equation for 1 buffalo that is equal to how many cows and then we can apply a unitary method. By doing this we will get as
 \[\begin{align}
  & \dfrac{7}{5}c=b \\
 & ?=35b \\
\end{align}\] . Thus, on solving we will get the same answer.