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ANSWERS - HURDLE 04 : LINEAR EQUATIONS
Ans 1. Solved as sample, in Hurdle 04.
Ans 2. i = idle, d= dosa, s= samosa.
3i + 4d + 5s = 274 ---(a)
2i + 3d + 4s = 210---- (b)
4i+ 3d+ 5s = 264 ---(c)
equation (c) - equation (a) = i -d = -10---- (x)
5b - 4c = -6i +3d = -6 or 2i - d = 2--- (y)
X- Y = i = 12
Put value of i in (x) d= 22
put value of i and d in (a) we get s= 30
So 2i + 4d + 6s = 292.
Ans 3. 4100
Ans 4. 280
Ans 5. 340
Ans 6. 350
Ans 7 . From first statement we get: 2H + 4 B + 8 F =
3600
Divide it by 2 we get :
H + 2B + 4F = 1800 = required answer.
Ans 8 . B = Basket, C = Cooker, M = Mug
1B + 3C + 4 M = 1900.....(p)
3B + 4C + 2M = 2700......(q)
4B + 3C+ 5M = 2900......(r)
Now,
equation r - equation p = 3B + M = 1000......(x)
3q- 4p = 5B - 10M =500......(y)
10x + y = 35B = 10500
so B = 300
put Value of B in (x) we get M = 100
Put value of B and M in (p) we get C
= 400
Now,
300 + 3* 400 + 100 M = 2500
so M = 10.
Ans 9 .
2B + 3P + 4H = 950 (1)
3B+ 4P + 2H = 875 (2)
1B+ 3P + 5H = 1000 (3)
From 1 and 3 we get H-B = 50 (4)
From 1 and 2 we get
10H -B = 1175 (5)
from 4 and 5 we get 9H= 1125
so H = 125 and B = 75 .
We get P as 100
To carry the minimum weight , you will have to check
if the maximum number of things that are lightest can
be carried most.
1225/75 = 16.33
If you buy 16 books , you will have balance Rs 25, you
cannot buy anything with remaining 25.
so you buy 15 books , you will have balance Rs. 100
with which you can buy 1 printer. So you weight will
be15*100 +150 = 1650
Now checking if by replacing some books by printer or
harddisk , you can reduce the weight :
1) If you buy 4 books less you can buy 3 printers
more. In that case the weight you will carry will be
11*100 + 4*150 = 1100 + 600 = 1700 , so this is more
than 1650.
2) Also checking if some books can be replaced with
Hard disk, the next best option will be to buy 5 books
less and 3 more Hard disk . In this case you will have
to carry 10 books + 1 printer + 3 hard disk which will
be 1000 + 150 + 600 = 1750 , which is again more than
1650.
3) Also you may check the possibility where you buy 3 books less and buy 1
printer and 1 hard disk more. The weight will be 12*100 + 150*2 +200 = 1700,
which is again more than 1650.
So the best option is to buy 15 books, 1 printer and
no hard disk. The minimum weight will be 1650 grams.
Ans 10 . Only 2 is definitely true. 1 may not be true
as in the last paragraph it is mentioned that there
were subtle difference in about 4 species.
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