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Q. A boat covers 24 km upstream and 18 km downstream in 6 hours, while it covers 36 km upstream and 36 km downstream in 10 hours. The speed of the current is:

Q. एक नाव 6 घंटे में धारा के विपरीत 24 किमी और धारा की दिशा में 18 किमी चलती है, जबकि धारा के विपरीत 36 किमी और धारा की दिशा में 36 किमी 10 घंटे में चलती है। धारा की गति है:

A

0.75 km/h
0.75 किमी / घंटा
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B

1.5 km/h
1.5 किमी / घंटा
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C

1 km/h
1 किमी / घंटा
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D

2 km/h
2 किमी / घंटा
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Solution

The correct option is B
1.5 km/h
1.5 किमी / घंटा
Method 1:
Let the speed of the boat be = x km/h
Let the speed of the stream be = y km/h
Speed of the boat against the stream will be = (x - y) km/h
Speed of the boat in the direction of the stream will be = (x + y) km/h
24(xy)+18(x+y)=6h(1)36(xy)+36(x+y)=10h(2)
For simplification,
Let us substitute, 1(xy)= m and 1(xy) = n.
Such that the equations will get reduced as:
24m + 18n = 6 --- (3)
36m + 36n =10 --- (4)
Equation (3) can further be simplified as: 4m+3n = 1 ----- (5)
Equation (4) can further be simplified as : 18m+18n = 5 ---- (6)
Multiplying Eq. (5) with 18 and Eq. (6) with 4 so as to solve the equations;
72m + 54n = 18 ---- (7)
72m + 72n = 20 ----- (8)
(8) - (7) = 18 n = 2
Thus, n = 218=19
m = (13n)4=(13×19)4=16
Thus, (13n)4=(13×(19)4
Similarly, m = 1(x+y)=19 x-y = 9
Adding the two equations, 2x = 6+ 9 =15, x = 7.5 km/hr
y = 1.5 km/hr

Method 2:
Downstream speed = x + y = (24×36)(36×18)(24×10)(36×6)=21624 = 9 km/hr ---> (1)
Upstream speed = x-y = ((18×36)(24×36))((18×10)(36×6))=21636 = 6 km/hr -----> (2)

Solving, y = 1.5 km/hr


विधि 1:
माना कि नाव की चाल = x km/h
माना कि धारा की चाल = y km/h
धारा के विपरीत नाव की चाल = (x - y) km/h
धारा के साथ नाव की चाल = (x + y) km/h

24(xy)+18(x+y)=6h(1)36(xy)+36(x+y)=10h(2)

हल करने की सुगमता के लिए,
1(xy)= m तथा 1(xy)= n मान लेते हैं,तो

24m + 18n = 6 --- (3)
36m + 36n =10 --- (4)
समीकरण (3) तथा समीकरण (4) को सरल करते हुए इस प्रकार भी लिख सकते हैं,

4m+3n = 1 ----- (5)
18m+18n = 5 ---- (6)

समीकरण (5) को 18 तथा समीकरण (6) को 4 से गुणा करने पर,

72m + 54n = 18 ---- (7)
72m + 72n = 20 ----- (8)
(8) - (7) = 18 n = 2,
n =n = 218=19
m = (13n)4=(13×19)4=16
इसी तरह,m = 1x+y=19 x-y = 9

दोनों समीकरणों को जोड़ने पर,2x = 6+ 9 =15, x = 7.5 km/hr
y = 1.5 km/hr

विधि 2:
धारा के साथ चाल = x + y = (24×36)(36×18)(24×10)(36×6)=21624 9 km/hr ---> (1)
धारा के विपरीत चाल = x-y = ((18×36)(24×36))((18×10)(36×6))=21636 = 6 km/hr -----> (2)
हल करने पर,y = 1.5 km/hr

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