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Question:

Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to

Explanation:

Let the weight and price of small box is ‘w’ and ‘p’ respectively.
∴ Selling price per gram for small box = p/w

Now, selling price per gram for large box = 0.88p/w

Also, selling price for the whole box = 2p.

⇒ Weight of the large box = $\frac{2 p}{0.88 p / w}$ = $\frac{2 w}{0.88}$ = $\frac{25 w}{11}$

∴ Required percentage = $\frac{\frac{25}{11} w - w}{w}$ × 100 = 14/11 × 100 ≈ 127%

Hence, option (a).

» Your doubt will be displayed only after approval.

Doubts

Praveen Jai Ram Raj said (2023-08-24 06:47:13)

What's the value of w??

Reply from Admin:

We cannot determine the value of w in this question. Though the question can be answered without knowing the value of w.

Farah said (2023-06-08 07:41:14)

how did we get the last step?

Reply from Admin:

Weight of the small box = w

Weight of the large box = 25w/11

We are asked the % by which weight of large box is greater than the weigh of the small box.

∴ Required % = $\frac{{Weight}_{Large box} - {Weight}_{Small box}}{{Weight}_{Small box}} \times 100 %$ = $\frac{\frac{25 w}{11} - w}{w} \times 100 %$ = $\frac{\frac{14 w}{11}}{w} \times 100 %$ = $\frac{14}{11} \times 100 %$ ≈ 127%

Farah said (2023-06-08 07:45:22)

how did the step "weight of the box come up?"

Reply from Admin:

Selling price per gram = $\frac{Total Selling price}{Total weight}$

⇒ Total weight = $\frac{Total Selling price}{Selling price per gram}$

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