NCERT SOLUTIONS FOR CLASS10TH MATHS NCERT CHAPTER 4 QUADRETIC EQUATION EX 4.2 QUESTION NUMBER 6
प्रश्न -(6 ) एक कुटीर उद्योग एक दिन में कुछ बर्तनो का निर्माण करता हे। एक विशेष दिन ये देखा गया की प्रत्येक नग की निर्माण लागत (रूपये में ) उस दिन के निर्माण किये गए बर्तनो की संख्या के दुगने से 3 अधिक थी। यदि उस दिन की कुल निर्माण लागत 90 रुपये थी , तो निर्मित बर्तनो की संख्या और प्रत्येक नग की लागत ज्ञात कीजिये ?
हल : माना की विशेष दिन निर्मित बर्तनो की संख्या X हे , तो प्रत्येक बर्तन की लागत = 2X +3 होगी।
अब कुल लागत = लागत दर * बर्तनो की संख्या
=> 90 = (2X +3 ) * X
=> 90 = 2X^2 + 3X
=> 0 = 2X^2 + 3X -90
=> 0 = 2X^2 +15X -12X -90
=> 0 = X (2X +15 ) -6 (2X +15 )
=> 0 = (2X +15 ) (X -6 )
2X +15 = 0 OR X -6 = 0
X = -15 /2 (IMPOSSIBLE ) OR X = 6 (बर्तनो की संख्या )
प्रति बर्तन लागत =2X + 3 = 2 * 6 + 3 = 12 + 3 = 15 : उत्तर
ENGLISH TRANSLATION
Question-(6) A cottage industry manufactures some utensils in a day. On a particular day it was observed that the manufacturing cost (in RUPEE ) of each piece was 3 more than twice the number of pots manufactured on that day. If the total manufacturing cost for that day was RUPEE 90, then find the number of utensils manufactured and the cost of each piece?
Solution: Let the number of utensils manufactured on a particular day be X, then the cost of each vessel will be = 2X +3.
Now total cost = cost rate * number of utensils
=> 90 = (2X +3 ) * X
=> 90 = 2X^2 + 3X
=> 0 = 2X^2 + 3X -90
=> 0 = 2X^2 +15X -12X -90
=> 0 = X (2X +15 ) -6 (2X +15 )
=> 0 = (2X +15 ) (X -6 )
2X +15 = 0 OR X -6 = 0
X = -15 /2 (IMPOSSIBLE ) OR X = 6 (Number of pots)
Cost per pot = 2X + 3 = 2 * 6 + 3 = 12 + 3 = 15 : Answer