Question

A man buys 13.23 Kg of one type of rice for Rs.30 per Kg and 15.45 Kg of another type of rice for Rs.67.99 per Kg. If he mixes them and makes packets, each containing 3450 g of rice, how many such packets of rice are there and what is the cost of each packet?

Answer 1

Hint: We use the unitary method to find the value of total cost of both types of rice separately and then add total quantities of both types of rice and add total cost of both types of rice. Convert the total weight obtained from both types of rice into grams and find the number of packets using the unitary method. Divide total cost obtained from addition of both types of rice by the number of packets to obtain price of each packet.
* Unitary method helps us to find the value of a single unit when we are given the value of multiple units and number of units by dividing value of multiple units by number of units.
* We can find the value of multiple units by multiplying the value of a single unit by number of units.
* 1 kilogram is 1000 grams

Complete step by step answer:
Let us denote the types of rice by A and B
Weight of type A rice is \[ = 13.23\]Kg
Cost of type A rice per Kg \[ = Rs.30\]per Kg
Use unitary method to find the cost of total weighing type A rice
Cost of 1 Kg of type A rice \[ = Rs.30\]
\[ \Rightarrow \]Cost of 13.23 Kg of type A rice \[ = Rs.(30 \times 13.23)\]
\[ \Rightarrow \]Cost of 13.23 Kg of type A rice \[ = Rs.396.9\] …………………..… (1)
Weight of type B rice is \[ = 15.45\]Kg
Cost of type B rice per Kg \[ = Rs.67.99\]per Kg
Use unitary method to find the cost of total weighing type B rice
Cost of 1 Kg of type B rice \[ = Rs.67.99\]
\[ \Rightarrow \]Cost of 15.45 Kg of type B rice \[ = Rs.(67.99 \times 15.45)\]
\[ \Rightarrow \]Cost of 15.45 Kg of type B rice \[ = Rs.1050.4455\] ………………….… (2)
Now we find the total weight of rice obtained after mixing them
Total weight \[ = \] weight of type A rice \[ + \]weight of type B rice
\[ \Rightarrow \]Total weight \[ = (13.23 + 15.45)\]Kg
\[ \Rightarrow \]Total weight \[ = 28.68\]Kg …………………..… (3)
Also, total cost of rice of both type from equations (2) and (3)
Total cost of rice after mixing both types of rice \[ = \]Total cost of type A rice \[ + \] Total cost of type B rice
\[ \Rightarrow \] Total cost of rice after mixing both types of rice \[ = Rs.(396.0 + 1050.4455)\]
\[ \Rightarrow \] Total cost of rice after mixing both types of rice \[ = Rs.1447.3455\] ……………………..… (4)
Since we have from equation (4), the total weight of rice in Kilograms, we convert the weight into grams.
Since, $1 Kg = 1000 g$
\[ \Rightarrow 28.68\]Kg \[ = 1000 \times 28.68\]g
\[ \Rightarrow 28.68\]Kg \[ = 28680\]g …………………….… (5)
Since, 1 packet is of weight 3450 g. So, we can find the number of packets that can be formed from the total weight of rice i.e. 28680 g
\[ \Rightarrow \]Number of packets that can be made of 3450 g each \[ = \dfrac{{28680}}{{3450}}\]
\[ \Rightarrow \]Number of packets that can be made of 3450 g each \[ = 8.3\]
We take approximate value of number of packets i.e. 8
We know from equation (4), the total cost of mixed rice is Rs.1447.3455
So, we can find the cost of each packet by dividing the total cost by the number of packets.
Price of 8 packets of mixed rice \[ = Rs.1447.3455\]
Using unitary method we can write
\[ \Rightarrow \]Price of 1 packet of mixed rice \[ = Rs.\left( {\dfrac{{1447.3455}}{8}} \right)\]
\[ \Rightarrow \]Price of 1 packet of mixed rice \[ = Rs.180.91\]

\[\therefore \] Number of packets is 8 and price of each packet is Rs.180.91

Note:
Students might make mistakes in the solution as they don’t convert the total weight from Kilograms (Kg) to grams (g) sometimes. Also, we take an approximate value of the number of packets because the number of packets obtained after division is in decimal form, so we take the number of complete packets formed. Students are advised to use calculators for division of numbers that have decimal numbers.