A had some chocolates, and he divided them into two lots A and B. He sold the first lot at the rate of ₹2 for 3 chocolates and the second lot at the rate of ₹1 per chocolate, and got a total of ₹400. If he had sold the first lot at the rate of ₹1 per chocolate, and the second lot at the rate of ₹4 for 5 chocolates, his total collection would have been ₹460. Find the total number of chocolates he had.

A had some chocolates, and he divided them into two lots A and B. He sold the first
lot at the rate of ₹2 for 3 chocolates and the second lot at the rate of ₹1 per chocolate, and got a total of ₹400. If he had sold the first lot at the rate of ₹1 per  chocolate, and the second lot at the rate of ₹4 for 5 chocolates, his total collection  would have been ₹460.
Find the total number of chocolates he had.

x = number of chocolates in lot A

y= number of chocolates in lot B

 ₹2 for 3 chocolates means (2/3) for 1 chocolate 

He sold the first lot at the rate of ₹2 for 3 chocolates and the second lot at the rate of ₹1 per chocolate, and
got a total of ₹400. 

so

{2/3}x+1y=400

multiplying  by 3 

2x+3y=1200-------------(1)

If he had sold the first lot at the rate of ₹1 per  chocolate, and the  second lot at the rate of ₹4 for 5 chocolates, his total collection  would have been ₹460

similary

1x +{4/5} y=460

multiplying by 5

5x+4y = 2300---------------------(2)

2x+3y=1200-------------(1)   *5

5x+4y = 2300---------------------(2)  *2

 

eliminating x 

10x +15y =6000

10x+8y=4600

---------------------------

subtracting

7y=1400

y=1400/7=200

substituting in (1)

2x+600=1200

2x =1200-600

2x=600

x=600/2

x=300

 

total number of chocolates = x+y =300+200 =500

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