Only for MODERATORS or EXPERTS. No spamming please. Very Important Questions 1.) At a certain time in a deer park, the number of heads and the number of legs of deer and human visitors were counted and it was found there were 39 heads & 132 legs. Find the number of deer and human visitors in the park. 2.) Solve for x, y41x + 53y = 135, 53x +41y =1479.. Find the value of p and q for which the system of equations represent coincident lines 2x +3y = 7, (p+q+1)x +(p+2q+2)y = 4(p+q)+1 3.) A motor boat can travel 30 km upstream and 28 km downstream in 7h. It can travel 21km upstream and return in 5h. Find the speed of the boat in still water and the speed of the Stream.
Answers
1.) let x be the total no of legs of deer
let y be the total no of legs of visitors.
∴x + y = 132
∵1deer has 4 legs and 1 head & 1 visitor has 2 legs and 1 head
∴x/4 + y/2 = 39
plotting the graph we get the point of intersection which is the value of x and y.
thus from the graph we can say x = 108 and y=24
∴ num of deers = 108/4 = 27
∴ num of visitors = 24/2 = 12
2.) 41x+53y=135------------ (1)
53x+41y=147-------------(2)
by elimination method,
multiply 41 in eq.(1) and multiply 53 in eq.(2),
(41x+53y=135)×41
(53x+41y=147)×53
1681x+2173y=5535
2809x+2173y=7791
__________________(by subtracting)
-1128x = -2256. (2173y-2173y cancelled)
x = -2256/-1128(- and - is cancelled
x = 2
put the value of x in eq. (2),
53x+41y=147
53×2+41y=147
106+41y=147
41y=147-106
41y=41
y=41/41
y=1
so the value of x=2
y=1 Ans.
3.) Let the speed of the stream = ykm/hr.
Speed upstream = x - y.
Speed Downstream = x + y.
Now,
Given that boat can travel 30km upstream and 28km downstream in 7 hours.
30/x-y + 28/x+y = 7
Let 1/x - y = a and 1/x + y = b
30a + 28b = 7 ---------------------------- (1).
Also, Given that it can travel 21 km upstream and return in 5 hours.
21/x - y + 21/x + y = 5
Let 1/x - y = a and 1/x + y = b
21a + 21b = 5 ------------------------ (2)
On solving (1) * 21 & (2) * 28, we get
630a + 588b = 147
588a + 588b = 140
-----------------------------
42a = 7
a = 1/6.
Substitute a = 6 in (1), we get
30a + 28b = 7
30(1/6) + 28b = 7
5 + 28b = 7
28b = 7 - 5
28b =2
b = 2/28
b = 1/14.
We know that,
a = 1/x - y
1/6 = 1/x - y
x - y = 6 ----------- (3)
We know that,
b = 1/x + y
1/14 = 1/x + y
x + y = 14 ------------ (4).
On solving (3) & (4), we get
x + y = 14
x - y = 6
------------
2x = 20
x = 10
Substitute x = 10 in (4), we get
x + y = 14
10 + y = 14
y = 14 - 10
y = 4.
Therefore the speed of the boat in still water = 10km/hr.
Therefore the speed of the stream = 4km/hr.
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