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Question
Three bags contain 64.2 kg of sugar. The second bag contains `4/5` of the contents of the first and the third contains `45 1/2`% of what there is in the second bag. How much sugar is there in each bag?
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Solution
The total weight of sugar in three bags = 64.2 kg
Let the first bag contains x kg sugar.
The second bag contains = `x xx 4/5 kg = (4x)/5 kg`
Third bag contains = `x xx 4/5 xx 91/2%`
= `x xx 4/5 xx (91/2)/100`
= `(91x)/250 kg`
According to the question,
`x + (4x)/5 + (91x)/250 = 64.2`
⇒ `(250x + 200x + 91x)/250 = 64.2`
⇒ 541x = 64.2 × 250
⇒ 541x = 16050
⇒ `x = 16050/541 = 29.67 kg`
So, first bag contains the sugar = 23.73 kg
Second bag contains the sugar = `29.67 xx 4/5 = 23.73 kg`
And third bag contains the sugar = `91/250 xx 29.67 = 10.8 kg`
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