In a certain town, 25% families own a phone and families 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:
1. 10% families own both a car and a phone.
2. 35% families own either a car or a phone.
3. 40,000 families live in the town.
Which of the above statements are correct?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

1 and 2

1 and 3

2 and 3

1,2 and 3

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$\begin{array}{l} n (P) = 25 %, n (C) = 15 %, \\ n (P^{c} \cap C^{c}) = 65 %, n (P \cap C) = 2000 \end{array}$

$\begin{array}{l} n (P^{c} \cap C^{c}) = 65 % \\ \Rightarrow n (P \cup C)^{c} = 65 % \\ \Rightarrow n (P \cup C) = 35 % \\ Now n (P \cup C) = n (P) + n (C) - n (P \cap C) \\ \Rightarrow 35 = 25 + 15 - n (P \cap C) \\ \Rightarrow n (P \cap C) = 40 - 35 = 5 \\ \Rightarrow 5 % of the total = 2000 \end{array}$

$\begin{array}{l} \Rightarrow Total number of families \\ = \frac{2000 \times 100}{5} = 40000 \end{array}$

Therefore, statements 2 and 3 are correct.

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET