EXERCISE 3.6 QUESTION 2 ALL SOLUTIONS MATHS CHAPTER 3
EXERCISE 3.6 QUESTION 2 CLASS 10TH
EXERCISE 3.6 CLASS 10 QUESTION 2 PART 1
EXERCISE 3.6 CLASS 10 QUESTION 2 PART 2
EXERCISE 3.6 CLASS 10 QUESTION 2 PART 3
प्रश्न -(2) निम्न समस्याओ को रेखिक समीकरण युग्म के रूप में व्यक्त कीजिये और फिर उनके हल ज्ञात कीजिये ?
(i) रितु धारा के अनुकूल 2 घंटे में 20 km तैर सकती हे और धारा के प्रतिकुल 2 घण्टे में 4 km तैर सकती हे। उसकी स्थिर जल में तेरने की चाल तथा धारा की चाल ज्ञात कीजिये।
हल : माना की रितु की स्थिर जल में तैरने की चाल x km / घंटा हे। एवं धारा की चाल y km / घंटा हे।
प्रश्नानुसार , धारा के अनुदिश , चाल x + y होगी। क्युकी इसमें
चाल = दूरी / समय
x + y = 20 / 2
x + y = 10 -----> (1)
एवं धारा के विपरीत दिशा में चाल x - y होगी।
चाल = दूरी / समय
x - y = 4 / 2
x - y = 2 -------> (2)
समीकरण (1 ) व (2) को जोड़ने पर ,
2x = 12
x = 12 / 2 =6
x = 6 km / hr = रितू की स्थिर जल में तैरने की चाल।
x का मान समीकरण (2 ) में रखने पर ,
x - y = 2
6 - y = 2
6 - 2 = y
4 = y
y = 4 km / hr = धारा की चाल
(ii) 2 महिलाओ एवं 5 पुरुष एक कसीदे के काम को साथ -साथ 4 दिनों में पूरा कर सकते हे जबकि
3 महिलाये और 6 पुरुष इसको 3 दिनों में पूरा कर सकती हे। ज्ञात कीजिये की इसी कार्य को करने में एक
अकेली महिला कितना समय लेगी। पुनः इसी कार्य को करने में एक पुरुष कितना समय लेगा।
हल : माना एक महिला अकेले एक कसीदे के कार्य को x दिन में तथा एक पुरुष अकेले उसी कार्य को y
दिन में पूरा करते हे , तो प्रश्नानुसार ,
Question-(2) Express the following problems in the form of a pair of linear equations and then find their solutions?
(i) RITU can swim 20 km downstream in 2 hours and 4 km upstream in 2 hours. Find his swimming speed in still water and the speed of the stream.
Solution : Let the speed of RITU swimming in still water be x km/hr. And the speed of the stream is y km / h.
According to the question, along the current, the speed will be x + y. because in this
speed = distance / time
x + y = 20 / 2
x + y = 10 -----> (1)
And the speed in the opposite direction of the current will be x - y.
speed = distance / time
x - y = 4 / 2
x - y = 2 -------> (2)
Adding equation (1) and (2),
2x = 12
x = 12 / 2 =6
x = 6 km / hr = RITU's swimming speed in still water.
Substituting the value of x in Equation (2),
x - y = 2
6 - y = 2
6 - 2 = y
4 = y
y = 4 km / hr = speed of stream
(ii) 2 women and 5 men can together complete a piece of work in 4 days while
3 women and 6 men can complete it in 3 days. Find out that in doing the same work, one
How long will a single woman take? How much time will one man take to do the same work again?
Solution : Let a woman alone do the work of a ballad in x days and a man alone in y days.
If you complete it in a day, then according to the question,
Let 1 / x = s and 1 / y = t then,
2s + 5t = 1/4 => 8s + 20t -1 = 0 ------> (3)
3s + 6t = 1 / 3 => 9s + 18t - 1 = 0 -------> (4)
x = 18 and y = 36 : Answer
(iii) ROOHI travels some distance by train and some distance by bus to reach her home situated at a distance of 300 km. If she travels 60 km by train and the rest by bus, it takes her 4 hours. If he travels 100 km by train and the rest by bus, it takes him 10 minutes more. train
and find the speed of the bus respectively.
Solution : Let the speed of the train be x km/hr and that of the bus be y km/hr.
When ROOHI covers a distance of 60 km by train, the bus will cover a distance of 300 - 60 = 240 km
So the journey will take 4 hours.
Therefore,
When ROOHI covers a distance of 100 km by train, then
Will cover a distance of 300 - 100 = 200 km by bus then travel time will take = 4 hours 10 minutes
In other words,
Let 1 / x = s and 1/ y = t then
15s + 60t = 1 => 15s + 60t -1 = 0 ------> (3)
24s + 48t = 1 => 24s + 48t -1 = 0 -------> (4)
Answer: The speed of the train is x = 60 km/hr and the speed of the bus is y = 80 km/hr.