Advertisements
Advertisements
Question
In the adjacent diagram, if n(U) = 125, y is two times of x and z is 10 more than x, then find the value of x, y and z
Advertisements
Solution
n(U) = 125
y = 2x and z = x + 10
n(U) = x + 4 + y + 17 + 3 + 6 + z + 5
125 = x + 4 + 2x + 17 + 3 + 6 + x + 10 + 5
125 = 4x + 45
125 – 45 = 4x
80 = 4x
x = `80/4` = 20
y = 2x
= 2 × 20
= 40
z = x + 10
= 20 + 10
= 30
∴ The value of x = 20, y = 40 and z = 30.
APPEARS IN
RELATED QUESTIONS
Write the cardinal number of the following set:
B = {-3, -1, 1, 3, 5, 7}
Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.
Find: n(A ∪ D)
If n(A) = 300, n(A ∪ B) = 500, n(A ∩ B) = 50 and n(B’) = 350, find n(B) and n(U)
In a class, all students take part in either music or drama or both. 25 students take part in music, 30 students take part in drama and 8 students take part in both music and drama. Find the number of students who take part in only music
In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspaper, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspaper and 3 families buy all the three newspaper. If each family buy atleast one of these newspaper then find Number of families buy only one newspaper
In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspaper, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspaper and 3 families buy all the three newspaper. If each family buy atleast one of these newspaper then find Total number of families in the colony
A survey of 1000 farmers found that 600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew ragi and corn, 80 grew paddy and corn. If each farmer grew atleast anyone of the above three, then find the number of farmers who grew all the three.
Each student in a class of 35 plays atleast one game among chess, carrom and table tennis. 22 play chess, 21 play carrom, 15 play table tennis, 10 play chess and table tennis, 8 play carrom and table tennis and 6 play all the three games. Find the number of students who play chess and carrom but not table tennis (Hint: Use Venn diagram)
If n(A ∪ B ∪ C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ∩ C) = 15, n(A ∩ C) = 25 and n(A ∩ B ∩ C) = 10, then the value of x is
If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ∩ L is
