NinetynineCAT 2021 Slot 3 QA Q17 Equations
Question 17 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.
A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is
TITA: type in the answer. There are no options and no negative marking.
Answer: 34 Equations TITA
Solution
- Let prices be \(2k, 5k, L\): \(10k^2 L = 800\).
- After the change: \((2k + 6)(5k + 6)L = 3200 = 4 \times 800\), so \((2k + 6)(5k + 6) = 40k^2\).
- \(10k^2 + 42k + 36 = 40k^2 \Rightarrow 5k^2 - 7k - 6 = 0 \Rightarrow k = 2\).
- Prices 4, 10 and \(L = \frac{800}{10 \times 4} = 20\); sum \(= 34\).