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A person spent ₹273 on buying a total of 50 packets of chips and biscuits. If the cost of each packet of chips is ₹6 and that of each biscuit packet is ₹5, then how many more biscuit packets than chips packets did he buy?
5
4
6
3
4
Assume all 50 were biscuit packets: 50×5=250. The difference is 273−250=23. Each chip packet costs ₹1 more than a biscuit packet, so there are 23 chip packets and 50−23=27 biscuit packets.
Total packets = 50, Total cost = ₹273, Cost of chips = ₹6/packet, Cost of biscuits = ₹5/packet.
6x+5y=273, x+y=50
Assume all 50 were biscuit packets: 50×5=250. The difference is 273−250=23. Each chip packet costs ₹1 more than a biscuit packet, so there are 23 chip packets and 50−23=27 biscuit packets.
Students often calculate the number of packets instead of calculating the difference between the two types as requested by the question.
Define variables
Let the number of chips packets be x and the number of biscuit packets be y. We are given x+y=50.
x+y=50
Set up cost equation
The total cost is the sum of the costs of individual packets: 6x+5y=273.
6x+5y=273
Solve the system
From the first equation, x=50−y. Substituting this into the second equation: 6(50−y)+5y=273, which simplifies to 300−6y+5y=273, so y=27.
y=27
Calculate chips packets
Substitute y=27 into x+y=50 to find x: x=50−27=23.
x=23
Find the difference
The question asks for how many more biscuit packets than chips packets: y−x=27−23=4.
27−23=4
B is correct because the number of biscuit packets is 27 and chips packets is 23, resulting in a difference of 4.
This problem can also be solved using the allegation method or a simple 'supposition' method, which is highly efficient for competitive exams involving two-variable item costs.
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