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Question
Hamid has three boxes of different fruits. Box A weighs `2 1/2` kg more than Box B and Box C weighs `10 1/4` kg more than Box B. The total weight of the three boxes is `48 3/4` kg. How many kilograms (kg) does Box A weigh?
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Solution
Let the weight of box A be x kg.
According to the question,
Weight of Box A = Weight of Box B + `5/2` kg ...[Given]
⇒ Weight of box B = `(x - 5/2)` kg
And weight of Box C = Weight of box B + `41/4` kg ...[Given]
⇒ Weight of Box C = `x - 5/2 + 41/4` kg
= `x + ((-10 + 41)/4)` kg
= `(x + 31/4)` kg
As, total weight of three boxes = `48 3/4` kg = `195/4` kg ...[Given]
∵ Total weight of three boxes = Weight of box A + Weight of box B + Weight of box C
∴ `195/4 = x + x - 5/2 + x + 31/4`
⇒ `195/4 = 3x + (31 - 10)/4`
⇒ `195/4 = 3x + 21/4`
⇒ `3x = 195/4 - 21/4`
⇒ `3x = (195 - 21)/4`
⇒ `3x = 174/4`
⇒ `x = 174/(3 xx 4)`
⇒ `x = 29/2`
∴ `x = 14 1/2` kg
Hence, box A weight `14 1/2` kg.
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