In the Sunday bazzar, Jamuna sells her lemons at Rs. 0.50 for two. Her neighbour Seema has a little smaller lemons; she sells hers at Rs. 0.50 for three. After a while, when both ladies have the same number of lemons left, Seema is called away. She asks her neighbour to take care of her goods. To make things simple, Jamuna puts all lemons in one big pile, and starts selling five lemons per one rupee. When Seema returns, at the end of the day, all lemons have been sold. But when they start dividing the money, there appears to be a shortage of Rs. 3.50. Supposing they divide the money equally, how much does Jamuna lose with this deal?
Let selling price per lemon of Jamuna be 'j' and that of Seema's be 's'.
Jamuna sells 2 lemons for Rs. 0.5 which makes j=(1/4)
Seema sells 3 lemons for Rs. 0.5 which makes s=(1/6)
After Seema leaves, Jamuna sells 5 lemons for a rupee and let it be denoted by t=(1/5)
Let the no. of lemons with each one of them be N.
If Seema would've sold her N lemons, she would've earned Rs. (N/6) and similarly, Jamuna would have earned Rs. (N/4).
When their individual stock is sold together, they earn Rs. (2N/5).
When counting, they observe that there's shortage of Rs. 3.50
So the eqn we can form is:
(2N/5)-(N/4)-(N/6) = 3.50
=> (N/60) = 3.5
=> N = 210 lemons
So, if Jamuna didn't sell both stocks together, she'd have earned Rs. (210/4) = Rs. 52.5
But on selling the stocks together and dividing the money equally, she gets Rs. ((2x210)/5) = Rs. 42ย
$$\therefore\ $$ Jamuna suffers a loss of Rs. 10.5
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