Question

please answer of following questions

Answer 1

10)
Time of Express train = Te
Time of Passenger train = Tp
Speed of Express train = Se
Speed of passenger train = Sp

An Express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore

Total distance, D = 132km

Time difference between Express train and passenger train is 1 hour
so, Tp-Te=1.........(1)

If the average speed of the Express train is 11kmph more than that of the passenger train
so, Sp = x
Se = Sp + 11
Se = x + 11

Te = D/Se = 132/(x+11)
Tp = D/Sp = 132/x

Te and Tp substitute in (1)

(132/x) - (132/(x+11))= 1
((132(x+11) - 132x)/(x+11)x) = 1
132(x+11-x) = x(x+11)
1452 = x² + 11x
x² + 11x - 1452 = 0
x² + 44x - 33x - 1452 = 0
x(x+44)-33(x+44) = 0
(x-33)(x+44) = 0
x + 44 = 0
x = - 44 Speed of the passenger train cannot be negative
so, Speed of passenger train is Se = x = 33 kmph
Speed of the Express train is Sp = x + 11 = 33 + 11 = 44 kmph

11)
Side of first square is a
Side of second square is b

Sum of the areas of two squares is 468m²

Area of first square = a²
Area of second square = b²

so, a² + b² = 468............(1)

if the difference of their perimeter is 24cm

Perimeter of first square = 4a
Perimeter of second square = 4b

so, 4a - 4b = 24
4(a - b) = 24
a - b = 6
a = b + 6...........(2)
(2) substitute in (1)

(b+6)² + b² = 468
b² + 12b + 36 + b² = 468
2b² + 12b = 468 - 36
2(b²+6b) = 432
b²+6b = 432/2
b²+6b = 216
b²+6b-216 = 0
b²+18b-12b-216=0
b(b+18)-12(b+18)=0
(b+18)(b-12)=0

b+18=0
b=-18
sides of second square cannot be negative value

b-12=0
b=12
side of second square is b = 12cm

b=12 in (2)
a = 12+6 = 18
side of first square is 18cm