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?

Answer 1

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`