IPMAT Indore 2024 - QA (MCQ) Q37 Explanation

Explanation:

(c) Let the number of apples and oranges be x and y.

Then the number of bananas = 𝑥 + 10.

Total number of fruits = 2x + y + 10

As per the question, x + (x + 10) = 11k (where k is a multiple of 11)

⇒ 2𝑥 + 10 = 11𝑘

⇒ 𝑘 = 2𝑥 + 10/11 ….(i)

Also, total fruits sold by the seller can be expressed in two ways. Equating both the expressions, we get

7𝑥/10 + 6/10 (𝑥+10) + 5/10 𝑦 = 55/100 (2𝑥 + 𝑦 + 10)

⇒ 14𝑥 +12𝑥 + 120 + 10𝑦 = 22𝑥 + 11𝑦 + 110

⇒ 4𝑥 + 10 = 𝑦…(ii)

Now, it is given that the fruit seller sold 70% of apples i.e. 7𝑥/10.

In order to keep this number an integer, x must be a multiple of 10.

The smallest value of x in eqn.(i), for which 𝑘 = 2𝑥+10/11 will be an integer is 50, a multiple of 10.

Substituting, 𝑥 = 50 in eqn.(ii), we get

y = 4(50) + 10 = 210 oranges. Ans