Q: When two armies met in combat, their men were divided in a 10:3 ratio. Their losses were 20:3 and their survivors were 40:13. Find the initial number of troops in each army if the number of survivors in the bigger army is 24,000?

A 28000, 8400
B 35600, 8400
C 34000, 8400
D 28000, 6200
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Answer: A


Let the soldiers in the two armies be 10X, 3X and losses be 20Y, 3Y,

Then we have,

survivors in the larger army

10X - 20Y = 24000 ...(i)

Likewise survivors in the smaller army

And 3X - 3Y = 24000 x 13/40 = 7800 -----(ii)

Solving, we have 10X = 28000, 3X = 8400

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Ratio and Proportion

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