ICSE Class 10 Answered
In a military camp, 50 officers had a choice of beans, plantain and rice. Of these officers,
21 chose beans, 24 plantain and18 rice. Also 3 chose beans only, 9 plantains only, 2 rice
only and 5 chose all three kinds of food.
(a). Illustrate the information on a Venn diagram
(b). Find the number of officers who chose plantain and beans only.
(c). How many officers chose exactly two kinds of food?
(d). How many officers chose none of the three kinds of food?
Asked by nuthanapeddinti.07 | 06 Dec, 2023, 03:49: PM
Expert Answer
Above venn diagram shows the type of food taken by military officers .
13 officers has taken Beans . 3 officers took Beans only .
24 officers has taken Plantain. 9 officers took Plantain only .
18 officers has taken rice . 2 officers has taken rice only.
5 officers has taken all three food .
Let x officers has taken Beans and Plantain . Let y oofficers has taken Bean and Rice .
Let z officers has taken Plantain and Rice .
Since 13 officers has taken beans , from the above information , we get
3+x+5+y = 13 or x+y = 5 .....................(1)
Since 24 officers has taken Plantain , from the above information , we get
9+x+5+z = 24 or x+z = 10 .....................(2)
Since 18 officers has taken Rice , from the above information , we get
2+y+5+z = 18 or y+z = 11 .....................(3)
By subtracting eqn.(1) from eqn.(3) , we get z - x = 6 ........................(4)
From eqn.(2) and (4) , we get z = 8 , x = 6 .
Hence from eqn.(3) , we get y = 3 .
------------------------------------------------------------------------------------------
Number of officers who has taken plantain and beans only = x = 6
Number of officers who has taken exactly two type of food = x+y+z = 6+3+8 = 17
----------------------------------------------------
Number of officers has taken exactly one type of food = 3+9+2 = 14
Number of officers has taken exactly two type of food = 2+3+8 = 13
Number of officers has taken all three type of food = 5
Number of officers has taken atleast one type of food = 14+13+5 = 32
Number of officers has not taken any food = 50 - 32 = 18
Answered by Thiyagarajan K | 06 Dec, 2023, 06:05: PM
Concept Videos
-
Cumulative Frequency Curve
Representation of cumulative frequency distribution with the help of ogiv... -
Representation of cumulative frequency distribution ...
Representation of cumulative frequency distribution with the help of ogive... -
Cumulative Frequency Curve: Exam Prep Strategies
Representation of cumulative frequency distribution with the help of ogive... -
Statistics: Graphical Representation
Statistics: Graphical Representation, Histogram and Ogive
ICSE 10 - Maths
Asked by nuthanapeddinti.07 | 06 Dec, 2023, 03:49: PM
ANSWERED BY EXPERTICSE 10 - Maths
Asked by rashikulkarni28 | 25 Jun, 2022, 06:44: PM
ANSWERED BY EXPERTICSE 10 - Maths
Asked by rashikulkarni28 | 25 Jun, 2022, 06:42: PM
ANSWERED BY EXPERTICSE 10 - Maths
Asked by rashikulkarni28 | 25 Jun, 2022, 06:40: PM
ANSWERED BY EXPERTICSE 10 - Maths
Asked by rashikulkarni28 | 25 Jun, 2022, 06:09: PM
ANSWERED BY EXPERTICSE 10 - Maths
Asked by kadtej83 | 15 Jul, 2019, 07:46: PM
ANSWERED BY EXPERTICSE 10 - Maths
Asked by Rayeesa | 10 Feb, 2018, 09:50: PM
ANSWERED BY EXPERT
