Question

The price of 7 bananas is equal to the cost of 3 kiwis. The price of 2 kiwis is equal to the cost of 1 banana and 5 chikoos. If Rambo has just enough money to buy 30 chikoos, then how many bananas Rambo could buy with the same amount?
A. 22
B. 20
C. 25
D. 11

Answer 1

Hint: We can assume the amount Rambo has as x and the cost of one banana as y. And after that we can make equations by first finding the cost of one chikoo using total amount as x and cost of 7 bananas, using that we can find the cost of kiwi in terms of y. Now we will get the linear equation of variable x and y when we put the cost of chikoo, banana and kiwi in the given condition (2 kiwi = 1 banana + 5 chikoo).

Complete step-by-step answer:
Let the amount Rambo has will be equal to Rs x.
As we know that from the Rs. x, Rambo can buy 30 chikoos.
So, the cost of one chikoo must be equal to Rs. \[\dfrac{x}{{30}}\].
Let the cost of one banana is equal to Rs. y
So, as given in the question, the price of 7 bananas is equal to the price of 3 kiwis.
So, the price of 7 bananas must be equal to (price of one banana)\[ \times \](7)
Price of 7 bananas = Rs. 7y
So, the price of 3 kiwis must be equal to Rs. 7y
As we know that if the price of n element of type A is equal to Rs B. Then the price of one element of type A must be equal to Rs. \[\dfrac{A}{n}\]
So, the price of one kiwi must be equal to Rs. \[\dfrac{{7y}}{3}\]
As given in the question, the price of 2 kiwis is equal to the cost of 1 banana and 5 chikoos.
So, solving the above equal. We get,
\[2 \times \dfrac{{7y}}{3} = y + \left( {5 \times \dfrac{x}{{30}}} \right)\]
Solving the above equation to find the y (i.e. cost of one banana).
\[\dfrac{{14y}}{3} = y + \dfrac{{5x}}{{30}}\]
Subtracting both sides of the above equation by y and then taking LCM on LHS of the equation. We get,
\[\dfrac{{14y - 3y}}{3} = \dfrac{{5x}}{{30}}\]
30(14y – 3y) = 5x(3)
330y = 15x
So, dividing both sides of the above equation by 15. We get,
x = 22y
Now as we know that Rambo had Rs. x and the cost of one banana is equal to Rs. y
And x = 22y.
So, Rambo can buy 22 bananas from Rs. x that is equal to the cost of 30 chikoos.
Hence, the correct option will be A.


Note:- Whenever we come up with this type of problem then first, we assume the total cost as Rs x. and then on dividing x by 30 (total number of chikoos) we will get the cost of one chikoo. After that we will assume the cost of one banana as Rs. y. And then find the cost of one kiwi in terms of y by solving the equation (cost of 3 kiwi = 7y). After that we can directly put the cost of chikoo, banana and kiwi in the equation (2 kiwis = 1 banana + 5 chikoos) and find the cost of banana in terms of (amount Ramboo had initially). This will be the easiest and efficient way to find the solution of the problem.