# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Ratio and Proportions Questions | Question 6

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Question 6 :Two types of tea A and B are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices per kg of A and B are in the ratio

1. 21 : 25
2. 19 : 24
3. 18 : 25
4. 17 : 25

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##### Method of solving this CAT Question from Ratio and Proportions

Let Tea A and B be sold at Rs.a and Rs.b respectively
When A and B are mixed in the ratio 3 : 2 and sold at a profit of 10% at Rs.40 per Kg
$$frac{3a + 2b}{5}$ = $\frac{40}{1.1}$ ------$1)
When A and B are mixed in the ratio 2 : 3 and sold at a profit of 5% at Rs.40 per Kg
$$frac{2a + 3b}{5}$ = $\frac{40}{1.05}$ ------$2)

Solving equations (1) and (2), we get
1.1 × ($$frac{3a + 2b}{5}$) = 1.05 ×$$$frac{2a + 3b}{5}$) $\frac{11}{10}$ ×$3a + 2b) = $$frac{21}{20}$ ×$2a + 3b)
66a + 44b = 42a + 63b
24a = 19b

$$frac{a}{b}$ = $\frac{19}{24}$ So, the cost prices per Kg of A and B are in the ratio 19 : 24 The question is "Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio" ##### Hence, the answer is 19 : 24 Choice B is the correct answer. ###### Signup and sample 9 full classes for freein Online CAT CoachingBest CAT Online Coaching Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sun, Jan 26th, 2020 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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