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CAT 2024 Slot 1 — QA Question 16

RatioEasy

 A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is

Answer & solution

Answer: 66

Solution

Medium

Set apples =5k=5k, mangoes =2k=2k from the given ratio; oranges are whatever remains of 187187. Apply the sales, then use the post-sale ratio 3:23:2 of unsold apples to unsold oranges to solve for kk.

1

Set up counts. Apples =5k=5k, mangoes =2k=2k, so oranges =187−7k=187-7k.

apples=5k, mangoes=2k, oranges=187−7k\begin{aligned} &\text{apples}=5k,\ \text{mangoes}=2k,\ \text{oranges}=187-7k \end{aligned}
2

Apply the sales. Unsold apples =5k−75=5k-75; unsold oranges =12(187−7k)=\tfrac12(187-7k).

5k−7512(187−7k)=32⇒ 2(5k−75)=3⋅12(187−7k)(cross-multiply)⇒ 10k−150=32(187−7k)⇒ 20k−300=561−21k(×2)⇒ 41k=861 ⇒ k=21\begin{aligned} &\dfrac{5k-75}{\tfrac12(187-7k)}=\dfrac32\\ &\Rightarrow\ 2(5k-75)=3\cdot\tfrac12(187-7k) \quad\text{(cross-multiply)}\\ &\Rightarrow\ 10k-150=\tfrac32(187-7k)\\ &\Rightarrow\ 20k-300=561-21k \quad\text{(}\times2\text{)}\\ &\Rightarrow\ 41k=861\ \Rightarrow\ k=21 \end{aligned}
3

Compute unsold fruits. With k=21k=21: oranges =187−147=40=187-147=40.

unsold apples=5(21)−75=30⇒ unsold mangoes=2(21)−26=16⇒ unsold oranges=12(40)=20⇒ total=30+16+20=66\begin{aligned} &\text{unsold apples}=5(21)-75=30\\ &\Rightarrow\ \text{unsold mangoes}=2(21)-26=16\\ &\Rightarrow\ \text{unsold oranges}=\tfrac12(40)=20\\ &\Rightarrow\ \text{total}=30+16+20=66 \end{aligned}
Total unsold fruits=66\text{Total unsold fruits}=66
CAT 2024 Slot 1 QA Q16: A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and m — Solution | TheCATExam