The total cost of 8 buckets and 5 mugs is 92 Rs. and the total cost of 5 buckets and 8 mugs is 77 Rs. Find the cost of 2 mugs and 3 buckets.

The total cost of 8 buckets and 5 mugs is 92 Rs. and the total cost of 5 buckets and 8 mugs is 77 Rs. Find the cost of 2 mugs and 3 buckets.
[A]30 Rs.
[B]35 Rs.
[C]38 Rs.
[D]70 Rs.

35 Rs.
C.P. of 1 bucket = x
C.P. of 1 mug = y
∴ 8x + 5y = 92 …..(1)
5x + 8y = 77 …..(2)
By using equation (1) \times 5 – equation (2) \times 8,
40x + 25y – 40x – 64y = 460 – 616
=> -39y = -156
=> y = 4
From equation (1),
8x + 20 = 92
=> 8x = 92 – 20 = 72
=> x = 9
∴ C.P. of 2 mugs and 3 buckets
= 2 \times 4 + 3 \times 9
= 8 + 27 = 35 Rs.
Hence option [B] is correct answer.

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