# Ranjana's mother gave her rupees 245 for buying new year cards .if she got some 10-rupee card ,2/3 as many 5 rupees cards, and 1/5 as many 15-rupee cards, how many of each kind did she buy?

1
by qwartile

2014-10-14T21:35:47+05:30

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Let number of 10 rupees cards = x
cost of 10 rupees card = 10x
number of 5 rupees cards = 2x/3
cost of 5 rupees card = 5(2x/3) = 10x/3
number of 15 rupees cards = x/5
cost of 10 rupees card = 15(x/5) = 3x

total cost = 10x + 10x/3 + 3x = (30x+10x+9x)/3 = 49x/3
thus 49x/3 = 245
⇒x = (245×3)/49
⇒x = 15 (no. of 10 rupees card)
2x/3 = (2×15)/3 = 10 (no. of 5 rupees card)
x/5 = 15/5 = 3 (no of 15 rupees card)
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