Question

A cake is cut into three pieces, whose weights are in the ratio 1:2:3. The heaviest of these three pieces is then further cut into four pieces with their weights in the ratio 1:2:3:4. If at the end of this process, the lightest piece obtained weights 24 grams, then find the weight of the original cake

Answer 1

Answer:

480 grams.

Step-by-step explanation:

Let the weight of the original cake is x.

If we cut it in the weight ratio 1:2:3, then the weight of the three pieces will be x/6, x/3, x/2 respectively.

Now the heaviest of those three pieces is x/2.

It is now divided into 4 pieces in the weight ratio 1:2:3:4.

Hence, the weight of the four pieces will be ($\frac{x}{2} *\frac{1}{10}$), ($\frac{x}{2} *\frac{2}{10}$), ($\frac{x}{2} *\frac{3}{10}$) and ($\frac{x}{2}*\frac{4}{10}$)  

or, x/20, x/10, 3x/20, and x/5 respectively.

So, finally, the smallest weight piece is x/20 which is equal to 24 gm.

Hence, x/20=24, ⇒ x= 480 grams.

Therefore, the weight of the original cake is 480 grams. (Answer)