Question 2 Formulate the following problems as a pair of equations, and hence find their solutions: (i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current. (ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. (iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Class 10 - Math - Pair of Linear Equations in Two Variables Page 67
Answers
and y km/h respectively.
Speed of Ritu while rowing
Upstream = (x - y) km/h
Downstream = (x + y) km/h
According to question,
2(x + y) = 20
⇒ x + y = 10 ... (i)
2(x - y) = 4
⇒ x - y = 2 ... (ii)
Adding equation (i) and (ii), we get
Putting this equation in (i), we get
y = 4
Hence, Ritu's speed in still water is 6 km/h and the speed of the current is 4 km/h.
(2)
Let the number of days taken by a woman and a man be x and y respectively.
Therefore, work done by a woman in 1 day = 1/x
According to the question,
4(2/x + 5/y) = 1
2/x + 5/y = 1/4
3(3/x + 6/y) = 1
3/x + 6/y = 1/3
Putting 1/x = p and 1/y = q in these equations, we get
2p + 5q = 1/4
By cross multiplication, we get
p/-20-(-18) = q/-9-(-18) = 1/144-180
p/-2 = q/-1 = 1/-36
p/-2 = -1/36 and q/-1 = 1/-36
p = 1/18 and q = 1/36
p = 1/x = 1/18 and q = 1/y = 1/36
x = 18 and y = 36
Hence, number of days taken by a woman = 18 and number of days taken by a man = 36
(3)
Let the speed of train and bus be u km/h and v km/h respectively.
According to the given information,
60/u + 240/v = 4 ... (i)
100/u + 200/v = 25/6 ... (ii)
Putting 1/u = p and 1/v = q in the equations, we get
60p + 240q = 4 ... (iii)
100p + 200q = 25/6
600p + 1200q = 25 ... (iv)
Multiplying equation (iii) by 10, we get
600p + 2400q = 40 .... (v)
Subtracting equation (iv) from (v), we get1200q = 15
q = 15/200 = 1/80 ... (vi)
Putting equation (iii), we get
60p + 3 = 4
60p = 1
p = 1/60
p = 1/u = 1/60 and q = 1/v = 1/80
u = 60 and v = 80
Hence, speed of train = 60 km/h and speed of bus = 80 km/h.
Answer:
Step-by-step explanation:
Ans. (i) Let speed of rowing in still water = x km/h
Let speed of current = y km/h
So, speed of rowing downstream = (x + y) km/h
And, speed of rowing upstream = (x − y) km/h
According to given conditions,
⇒ 2x + 2y = 20 and 2x − 2y = 4
⇒ x + y = 10 … (1) and x – y = 2 … (2)
Adding (1) and (2), we get
2x = 12⇒ x = 6
Putting x = 6 in (1), we get
6 + y = 10
⇒ y = 10 – 6 = 4
Therefore, speed of rowing in still water = 6 km/h
Speed of current = 4 km/h
NCERT Solutions for Class 10 Maths Exercise 3.6
(ii) Let time taken by 1 woman alone to finish the work = x days
Let time taken by 1 man alone to finish the work = y days
So, 1 woman’s 1-day work = ()th part of the work
And, 1 man’s 1-day work = ()th part of the work
So, 2 women’s 1-day work = ()th part of the work
And, 5 men’s 1-day work = ()th part of the work
Therefore, 2 women and 5 men’s 1-day work = (+)th part of the work… (1)
It is given that 2 women and 5 men complete work in = 4 days
It means that in 1 day, they will be completing th part of the work … (2)
Clearly, we can see that (1) = (2)
⇒ … (3)
Similarly, … (4)
Let
Putting this in (3) and (4), we get
2p + 5q = and 3p + 6q =
⇒ 8p + 20q = 1 … (5) and 9p + 18q = 1 … (6)
Multiplying (5) by 9 and (6) by 8, we get
72p + 180q = 9 … (7)
72p + 144q = 8 … (8)
Subtracting (8) from (7), we get
36q = 1⇒ q =
Putting this in (6), we get
9p + 18 () = 1
⇒ 9p = ½⇒ p =
Putting values of p and q in , we get x = 18 and y = 36
Therefore, 1 woman completes work in = 18 days
And, 1 man completes work in = 36 days
NCERT Solutions for Class 10 Maths Exercise 3.6
(iii) Let speed of train = x km/h and let speed of bus = y km/h
According to given conditions,
Let
Putting this in the above equations, we get
60p + 240q = 4 … (1)
And 100p + 200q = … (2)
Multiplying (1) by 5 and (2) by 3, we get
300p + 1200q = 20 … (3)
300p + 600q = … (4)
Subtracting (4) from (3), we get
600q = 20 − = 7.5
⇒ q =
Putting value of q in (2), we get
100p + 200 () =
⇒ 100p + 2.5 =
⇒ 100p = – 2.5
⇒ p =
But
Therefore, x =km/h and y = km/h
Therefore, speed of train = 60 km/h
And, speed of bus = 80 km/h
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