Home
Class 12
MATHS
A survey of 100 people shows that 63% of...

A survey of 100 people shows that `63%` of the Americans like cheese where as `76%` like apples. If `x%` of the Americans like both cheese and apples then value of x

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will use the principle of inclusion-exclusion in set theory. Here's a step-by-step solution: ### Step 1: Define the Variables Let: - \( P \) = Total number of people surveyed = 100 - \( N(C) \) = Number of people who like cheese = 63% of 100 = 63 - \( N(A) \) = Number of people who like apples = 76% of 100 = 76 - \( N(C \cap A) \) = Number of people who like both cheese and apples = \( x \% \) of 100 = \( x \) ### Step 2: Apply the Inclusion-Exclusion Principle According to the principle of inclusion-exclusion, the total number of people who like either cheese or apples (or both) can be expressed as: \[ N(C \cup A) = N(C) + N(A) - N(C \cap A) \] Substituting the values we have: \[ 100 = 63 + 76 - x \] ### Step 3: Simplify the Equation Now, simplify the equation: \[ 100 = 139 - x \] ### Step 4: Solve for \( x \) Rearranging the equation to isolate \( x \): \[ x = 139 - 100 \] \[ x = 39 \] ### Conclusion Thus, the value of \( x \) (the percentage of Americans who like both cheese and apples) is **39%**. ---
Promotional Banner

Similar Questions

Explore conceptually related problems

A survey shows that 63% of the Americans like cheese whereas 76% like apples , If x% of the Americans like both cheese and apples , then find value of x .

A survey shows that 63% of the Americans like cheese 4 whereas 76% like apples. If x% of the Americans likes both cheese and apples, find the value of x. (39<=x<=63)

It is known from a survey that 60% American like mangoes and 70% like apples. How many per cent of Americans like both mangoes and apples ?

A survey shows that 76% of the Indians like oranges, whereas 62%like bananas. What percentage of the Indians like both oranges and bananas?

A survey shows that 69% students like mathematics, whereas 75% like chemistry. If x% students like both the subjects, then the maximum value of x is

A survey shows that 63% of the people watch a news channel whereas 76% watch another channel. If x% of the people watch both channel then(a) x = 35 (b)x = 63 (c) 39≤x≤63(d) x = 39

A survey shows that 63 % of the pepole watch a news channel whereas , 76 % watch an entertiament channel at a particular time If X% of the pepole watch both types of channels , then

A survey of 40 children showed that 25% liked playing football. Howmany children liked playing football

If 60% people in a city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people are 50 lakh, find the exact number who like each type of game.

In a survey of 400 students of a school, it is found that 100 students like apple juice, 150 like orange juice and 75 like both. Find how many students do like neither apple not orange juice ?