Question

Two horses cost as much as 5 doges, 6 doges as much as 8 oxen, 10 oxen as much as 50 sheep, 14 sheep as much as 9 goats. If the price of one goat is Rs.700, find the cost of one horse.

Answer 1

Hint: These problems are nothing but ratio and proportion problems in which variables play a key role.
As given in the question the costs of various animals have been given in terms of comparison like 2 horses cost as much as 5 dogs, in this we will have different variables for each animal say D for dogs and H for horses so like this we have to assign various variables to every animal and find the values using ratios.

Complete step-by-step answer:
Let’s assume cost of the animals to be as follows:
Horse as H, Dog as D, Oxen as O, Sheep as S & Goat as G.
Now from the question we have the following equations using the variables assigned.
\[\begin{array}{*{20}{l}}
  {2{\text{ }}H{\text{ }} = {\text{ }}5{\text{ }}D - - - (1)} \\
  {6{\text{ }}D{\text{ }} = {\text{ }}8{\text{ }}O - - - (2)} \\
  {10{\text{ }}O{\text{ }} = {\text{ }}50{\text{ }}S - - (3)} \\
  {14{\text{ }}S{\text{ }} = {\text{ }}9{\text{ }}G - - - (4)}
\end{array}\]
Also we know that the cost of one goat is 700.
So, $G = 700$
Therefore, when we use this value in the above equation 4 we will ger
$
  S = \dfrac{{G \times 9}}{{14}} \\
  S = \dfrac{{700 \times 9}}{{14}} \\
  S = 45 \;
$
Similarly, we will do the same step by choosing the appropriate equation and we will get:
$
  O = \dfrac{{50 \times S}}{{10}} \\
  O = \dfrac{{50 \times 45}}{{10}} \\
  O = 225 \\
  D = \dfrac{{8 \times O}}{6} \\
  D = \dfrac{{8 \times 225}}{6} \\
  D = 300 \\
  H = \dfrac{{5 \times D}}{2} \\
  H = \dfrac{{5 \times 300}}{2} \\
  H = 750 \;
$
Therefore, we have the value of the H which is nothing but the Cost of horses.
From the above calculations we got the following data:
Cost of Horse: 750
Cost of Dog: 300
Cost of Oxen: 225
Cost of Sheep: 45
Cost of Goat: 70
So, the correct answer is “RS.750”.

Note: In this problem one should be focused on how to solve the equations to find the solution or the value of certain variable. Hence when we deal these kin of problems people most of the time get confused with the variable substation and value calculation. So try doing it efficiently so that there won’t be any errors in the answer.