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CAT 2021 Slot 1 — QA Question 18

Percentage ChangeEasy

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

Answer & solution

  • 127

  • B

    135

  • C

    144

  • D

    124

Solution

Easy

Let the small box have weight ww and price pp, so its price per gram is p/wp/w. Express the large box's per-gram price (12%12\% less) and its total price (twice pp), then solve for the large box's weight and compare it with ww.

1

Per-gram prices. Small box: p/wp/w per gram. Large box is 12%12\% cheaper per gram.

large price/gram=0.88⋅pw\begin{aligned} &\text{large price/gram}=0.88\cdot\frac{p}{w} \end{aligned}
2

Large box weight. Its total price is 2p2p, so weight =total priceprice/gram=\dfrac{\text{total price}}{\text{price/gram}}.

Wlarge=2p0.88 (p/w)=2w0.88=2w2225=25w11\begin{aligned} &W_{\text{large}}=\frac{2p}{0.88\,(p/w)}=\frac{2w}{0.88}=\frac{2w}{\frac{22}{25}}=\frac{25w}{11} \end{aligned}
3

Percentage excess over the small box weight ww.

25w11−ww×100=1411ww×100=1411×100⇒ =127.27…%≈127%\begin{aligned} &\frac{\frac{25w}{11}-w}{w}\times100=\frac{\frac{14}{11}w}{w}\times100=\frac{14}{11}\times100\\ &\Rightarrow\ =127.27\ldots\%\approx 127\% \end{aligned}
≈127% (option a)\approx 127\%\ \text{(option a)}

Total money doubles while per-gram price falls to a factor 0.880.88, so weight scales by 20.88=2511≈2.27\tfrac{2}{0.88}=\tfrac{25}{11}\approx2.27 — i.e. about 127%127\% more.

CAT 2021 Slot 1 QA Q18: Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice th — Solution | TheCATExam