Question

The price of \[349\] coconuts is \[Rs.2094\] . What will be the price of \[26\] dozens of coconuts ?
\[(1)\] \[Rs.1248\]
\[(2)\] \[Rs.1982\]
\[(3)\] \[Rs.1872\]
\[(4)\] \[Rs.1524\]

Answer 1

Hint: We have to find the price of \[26\] dozens of coconuts when we are given the price for \[349\] coconuts . We solve this question using the concept of fundamental solving the equations , we should also know the count of units which are stated as a dozen . Using the given data of price for \[349\] coconuts , We can calculate the price of one coconut and then we will multiply the price of one coconut with the total number of coconuts in 26 dozens to calculate the total price of \[26\] dozens of coconuts .

Complete step-by-step solution:
Given :
\[The{\text{ }}price{\text{ }}of{\text{ }}349{\text{ }}coconuts{\text{ }} = {\text{ }}Rs{\text{ }}2094\]
So , from the given expression we can compute the price of one coconut which we get as :
\[The{\text{ }}price{\text{ }}of{\text{ }}1{\text{ }}coconut{\text{ }} = {\text{ }}Rs{\text{ }}\dfrac{{2094}}{{39}}\]
On , solving we get the price of 1 coconut as :
\[The{\text{ }}price{\text{ }}of{\text{ }}1{\text{ }}coconut{\text{ }} = {\text{ }}Rs{\text{ }}6\]
Now , we also know that the count of units in a dozen is \[12\] .
So , we can calculate the total number of coconuts in \[26\] dozens as :
\[Number{\text{ }}of{\text{ }}coconuts{\text{ }}in{\text{ }}26{\text{ }}dozens{\text{ }} = {\text{ }}26 \times 12\;\]
\[Number{\text{ }}of{\text{ }}coconuts{\text{ }}in{\text{ }}26{\text{ }}dozens{\text{ }} = {\text{ }}312\]
Now , we can compute the total prize of the coconuts as :
\[The{\text{ }}total{\text{ }}price{\text{ }}of{\text{ }}26{\text{ }}dozens{\text{ }}of{\text{ }}coconuts{\text{ }} = {\text{ }}cost{\text{ }}of{\text{ }}1{\text{ }}coconut \times number{\text{ }}of{\text{ }}coconuts{\text{ }}in{\text{ }}26{\text{ }}dozens\]
\[The{\text{ }}total{\text{ }}price{\text{ }}of{\text{ }}26{\text{ }}dozens{\text{ }}of{\text{ }}coconuts = Rs{\text{ }}6 \times 312\]
\[The{\text{ }}total{\text{ }}price{\text{ }}of{\text{ }}26{\text{ }}dozens{\text{ }}of{\text{ }}coconuts = Rs{\text{ }}1872\]
Hence , the price of \[26\] dozens of coconuts is \[Rs{\text{ }}1872\] .
Thus , the correct option is \[\left( 3 \right)\] .

Note: The concept used to solve the question is known as direct proportion . The concept states that the relation between two variables whose ratio is equal to a constant value . In simple words , it states that changing the value of one of the two variables would affect the value of the other variable . As in the given question , if we decrease the value of the number of coconuts then the price of the coconuts would also decrease . As the value of the price and the number of coconuts are directly proportional to each other . A change in any one affects the value of the other .