In a school of student strength 500, two-thirds of the students, who do not wear spectacles do not bring lunch. Three-Quarters of the students who do not bring lunch, do not wear spectacles. Altogether there are 60 students who wear spectacles and do not bring lunch together. If K is the number of students who do not wear spectacles and do not bring lunch, then K/10 is ____.
Answers
Given : In a school of student strength 500, two-thirds of the students, who do not wear spectacles do not bring lunch. Three-quarters of the students, who do not bring lunch. do not wear spectacles
Altogether there are 60 students who wear spectacles and do not bring lunch together
To find : K/10 , K is the number of students who do not wear spectacles and do not bring lunch.
Solution:
Let say Students Wear spectacles = S
Students Do not Wear spectacles = 500 - S
Two-thirds of the students, who do not wear spectacles do not bring lunch
= ( 2/3) (500 - S)
Students bring Lunch = L
Students do not bring Lunch = 500 - L
Three-quarters of the students, who do not bring lunch. do not wear spectacles = (3/4)(500 - L )
do not wear spectacles do not bring lunch
= ( 2/3) (500 - S) = (3/4)(500 - L )
=> 8 ( 500 - S) = 9 (500 - L)
=> 9L = 8S + 500
Altogether there are 60 students who wear spectacles and do not bring lunch together
students who wear spectacles and do not bring lunch together = (1/4)(500 - L )
=> (1/4)(500 - L ) = 60
=> 500 - L = 240
=> L = 260
9L = 8S + 500
=> 9 * 260 = 8S + 500
=> S = 230
do not wear spectacles do not bring lunch = (3/4)(500 - L ) = ( 2/3) (500 - S)
= 180
K is the number of students who do not wear spectacles and do not bring lunch
=> K = 180
K/10 = 180/10 = 18
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