Relative speed =65-45km/hr
Relative speed=20km/hr
Convert to m/s
S=20*5/18
S=5.555
Length of the faster train =5.55555*18seconds
=100meters
c
Hint: Assume that the speed of the stream is x and the speed of the boat in still water is x. From the statement of the question form two equations in two variables x and y. This system is reducible to linear equations in two variables. Reduce the system to a system of linear equations in two variables by proper substitutions. Solve the system of equations using any one of the methods like Substitution method, elimination method, graphical method or using matrices. Hence find the value of x satisfying both the equation. The value of x will be the speed of the stream.
Complete step-by-step answer:
Let the speed of the stream be x, and the speed of the boat in still water be y.
We have the speed of the boat upstream = y-x.
Speed of the boat downstream = y+ x.
Now since it takes 14 hours to reach a place at a distance of 48 km and come back, we have the sum of the times taken to reach the place downstream and time taken to return back upstream is equal to 14.
Now, we know that time =Distance speed
Using, we get
Time taken to reach the place =48y+x and the time taken to return back =48y−x.
Hence, we have
48y+x+48y−x=14
Dividing both sides by 2, we get
24y+x+24y−x=7 —–(i)
Also, the time taken to cover 4km downstream is equal to the time taken to cover 3km upstream.
Hence, we have 4y+x=3y−x
Transposing the term on RHS to LHS, we get
4y+x−3y−x=0 ——– (ii)
Put 1y+x=t and 1y−x=u, we have
24t+24u=7 ——-(iii)4t−3u=0 ——–(iv)
Multiplying equation (iv) by 6 and subtracting from equation (iii), we get
24t−24t+24u+18u=7⇒42u=7
Dividing both sides by 42, we get
u=742=16
Substituting the value of u in equation (iv), we get
4t−3(16)=0⇒4t−12=0
Adding 12 on both sides, we get
4t=12
Dividing both sides by 4, we get
t=18
Reverting to original variables, we have
1y+x=18 and 1y−x=16
Taking reciprocals on both sides in both equations, we have
y+ x=8 ——- (v)y−x=6 ——–(vi)
Adding equation (v) and equation (vi), we get
2y=14
Dividing both sides by 2, we get
y=7.
Substituting the value of y in equation (v), we get
7+x=8
Subtracting 7 from both sides we get
x = 8-7 =1
Hence the speed of the stream is 1 km/hr.
1267
1620
twenty members
u c 5 numbers…..
we add the combination of digits…..
a.17->1+7=8(even)
b.23->2+3=5(odd)!!!!!
c.37->3+7=10(even)
d.13->1+3=4(even)
e.73->7+3=10(even)
all combinations are even xept 23
ans:23
7/5 * 5/q = 7/10
35/5q = 7/10
q=10
7 months
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810
time (dist covrd by husband) (dist covrd by wife)
0.5hr 20 miles 0 miles
1 hr 40 miles 25 miles
1.5 hr 60 miles 50 miles
2 hrs 80 miles 75 miles
2.5 hrs 100 miles 100 miles
Therefore wife catches up after 2.5 hrs..
1.5
Solution:
As given, we have,
The cost of one pen = 36 Rs.
So, the cost of 15 pens = 36 × 15 = 540 Rs.
The cost of one book = 45 Rs.
So, the cost of 12 books = 45 × 12 = 540 Rs.
The cost of one pencil = 8 Rs.
So, the cost of 10 pencils = 8 × 10 = 80 Rs.
Now,
the cost of each eraser is 40 Rs. less than the combined costs of pen and pencil.
So,
Combined costs of pen and pencil = 36 + 8 = 44 Rs.
Cost of one eraser = 44 – 40 = 4 Rs.
So, the cost of 5 erasers = 4 × 5 = 20 Rs.
Hence,
The total amount spent is
Hence, the total amount spent is 1180 Rs.