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Ratio Problem

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by capthan » Thu Mar 03, 2011 2:06 am
Linda earns $24,000 in June, July, and August. The ratio of June to the ratio of July and August is 2/3 and the ratio of July to ratio of August and June is 7/5. How much she earns in August?

Fast(within 2 mins) and efficient method to solve this and similar problems, please.
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by Anurag@Gurome » Thu Mar 03, 2011 2:33 am
capthan wrote:Linda earns $24,000 in June, July, and August. The ratio of June to the ratio of July and August is 2/3 and the ratio of July to ratio of August and June is 7/5. How much she earns in August?

Fast(within 2 mins) and efficient method to solve this and similar problems, please.
Let Linda earns $x, $y and $z in June, July, and August respectively.
Then x + y + z = $24,000
x: (y + z) = 2:3 implies x: (24000 - x) = 2:3 implies x = $9,600
y: (x + z) = 7:5 implies y: (24000 - y) = 7:5 implies y = $14,000
Hence z = 24000 - (9600 + 14000) = $400
Therefore, Linda earns $400 in August.
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by GMATGuruNY » Thu Mar 03, 2011 3:51 am
capthan wrote:Linda earns $24,000 in June, July, and August. The ratio of June to the ratio of July and August is 2/3 and the ratio of July to ratio of August and June is 7/5. How much she earns in August?

Fast(within 2 mins) and efficient method to solve this and similar problems, please.
Convert the ratios to fractions.

June:(July+August) = 2:3.
Since 2+3 = 5, June = 2/5 of the total.
June = 2/5 * 24,000 = 9600.

July:(August+June) = 7:5.
Since 7+5 = 12, July = 7/12 of the total.
July = 7/12 * 24,000 = 14,000.

Thus, August = Total - June - July = 24,000 - 9600 - 14,000 = 400.
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