Question

50 kg of wheat costs 400. How much will 70 kg of wheat cost? Bills​

Answer 1

Answer:

Rs. 560

Step-by-step explanation:

As per the provided information in the given question, we have :

• 50 kg of wheat costs 400.

We are asked to calculate the cost of 70 kg of wheat.

Basically, in order to calculate the cost of 70 kg of wheat, we'll be using the unitary method. Firstly, we'll find the cost of 1 kg of wheat and then we'll multiply it with 70 to find the cost of 70 kg of wheat. Well, we can also solve this question using the concept of direct variation. Let's solve by both methods!

$\underline{\small \sf {\maltese \; \; \; By \: unitary \: method : \; \; \; }}$

As in the question, it is stated that the cost of 50 kg of wheat is Rs. 400. So, we can say that,

$\longrightarrow \sf{\quad {Cost_{(1 \; kg)} = Rs. \; \cancel{\dfrac{ \; 400}{50}} }}$

Dividing 400 by 50.

$\longrightarrow \sf{\quad {Cost_{(1 \; kg)} = Rs. \; 8 }}$

Therefore, the cost of 1 kg of wheat is Rs. 8. Now, if the cost of 1 kg of wheat is Rs. 8. Then,

$\longrightarrow \sf{\quad {Cost_{(70 \; kg)} = Cost_{(1 \; kg)} \times 70 }}$

Substitute the values.

$\longrightarrow \sf{\quad {Cost_{(70 \; kg)} = Rs. \; 8 \times 70 }}$

Multiplying the terms.

$\longrightarrow \quad \underline{\boxed{\textbf{\textsf{Cost}}_{\textbf{\textsf{(70 \; kg)}}} = \textbf{\textsf{Rs. \; 560}}}}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

$\underline{\small \sf {\maltese \; \; \; By \: direct \: variation : \; \; \; }}$

Here, if the amount increases, the cost also increases. So, it is the case of direct variation. Note that :

$\sf{If \: x \: and \: y \: are \: in \: variation,then} \\ \\ \bull \: \: \: \sf{ \dfrac{x_1}{y_1} = \dfrac{x_2}{y_2} = \dfrac{x_3}{y_3} = \dfrac{x_n}{y_n} }$

Let the cost of 70 kg of wheat be Rs. x.

Constructing the table;

$\boxed {\begin{array}{c|c|c} \underline{\sf{ Amount_{(rice)} \; (in \; kg)}} & \underline{\sf{50 }} & \underline{\sf{70 }} \\ \\ \underline{\sf{Cost \: (in\: Rs.) }} & \underline{\sf{400}} & \underline{\sf{x}}\end{array} }$

Now,

$\longrightarrow \sf{\quad {\dfrac{50}{400} = \dfrac{70}{x} }}$

Cross multiply the values.

$\longrightarrow \sf{\quad { 50(x) = 70(400) }}$

Performing multiplication in LHS and RHS.

$\longrightarrow \sf{\quad { 50x = 28000 }}$

Transposing 50 from LHS to RHS, its arithmetic operator will get changed.

$\longrightarrow \sf{\quad { x = \cancel{\dfrac{28000}{50}} }}$

Dividing the terms.

$\longrightarrow \sf{\quad {x = 560 }}$

Therefore,

$\longrightarrow \quad \underline{\boxed{\textbf{\textsf{Cost}}_{\textbf{\textsf{(70 \; kg)}}} = \textbf{\textsf{Rs. \; 560}}}}$