Question

A, B and C rent a land, A puts 10 tractors for 7 months, B puts 12 tractors for 5 months and C puts 15 tractors for 3 months, if the rent of the land is Rs. 175000, how much does C pay as his share of rent?
$\left( A \right)$ 45000
$\left( B \right)$ 50000
$\left( C \right)$ 57000
$\left( D \right)$ 64000

Answer 1

Hint – In this particular question the ratio of their individual share is the multiplication of the individual tractors and the individual respective months (i.e. A : B : C = (A’s tractor multiplied by his respective month) : (B’s tractor multiplied by his respective month) : (C’s tractor multiplied by his respective month)) so use this concept to reach the solution of the question.

Complete step-by-step answer:
Given data:
A, B, and C rent a land,
A puts 10 tractors for 7 months, B puts 12 tractors for 5 month and c puts 15 tractors for 3 months.
So the ratio of the investment on the land is the multiplication of the individual tractors and the respective months.
So the ratio is,
A : B : C = (A’s tractor multiplied by his respective month) : (B’s tractor multiplied by his respective month) : (C’s tractor multiplied by his respective month)
Therefore, A : B : C = $\left( {10 \times 7} \right):\left( {12 \times 5} \right):\left( {15 \times 3} \right)$
Now simplify this we have,
Therefore, A : B : C = $\left( {70} \right):\left( {60} \right):\left( {45} \right)$
Now divide by 5 throughout the ratio we have,
Therefore, A : B : C = $\left( {14} \right):\left( {12} \right):\left( 9 \right)$
Now it is given that the rent of the land is Rs. 175000.
Now we have to find out how much C pays as his share of rent?
Now the share of the C which he has to pay is C’s ratio divided by the sum of the ratio multiplied by the rent of the land.
Therefore, the share of the C which he has to pay is = $\dfrac{9}{{14 + 12 + 9}} \times 175000$
Now simplify the above equation we have,
Therefore, the share of the C which he has to pay is = $\dfrac{9}{{35}} \times 175000$
$ \Rightarrow 9 \times 5000 = 45000$ Rs.
So this is the required share of the C which he has to pay.
Hence option (A) is the correct answer.

Note – Whenever we face such types of questions the key concept we have to remember is that if the total rent of the land is Rs. x and the share ratio of A, B and C is p: q: r than the share of the C is C’s ratio divided by the sum of the ratio multiplied by the rent of the land (i.e.$\dfrac{r}{{p + q + r}} \times x$), so simply substitute the values in this equation and simplify we will get the required answer.