6) Two cyclists start from the same point, at the same time one goes due north and the
other due west, along straight highways. Also, the speed of one cyclist is 5 km/hr. more than the other. If after two hours, hey
are 50 km apart from each other. Find the average speed of each cyclist.
7) The sum of the present ages of father and his son is 45 years. Five years ago, the product of their ages was 34 years. Find
their present ages.
8) The area of an exhibition hall is 96 sq. m. If the length and bredth be increased by 1 m. each, the area increases by 21 sq. m. Find
the length and breadth of the hall.
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6) let speed be v and v+5
as the cyclists go in prependicular directions so we have to use pythagoras to find there distance in form of v
(2v)^2 + (2v+10)^2 = (50)^2 implies v= 15
7) 34= 34 × 1 or 17×2
no other case
17×2 does not satisfy sum of ages condition
therefore answer is 39 and 6
8) let length and breadth be l and b
lb = 96
(l+1)(b+1)=117 implies
lb + l + b +1= 117
l+b = 20,
(l+b)^2 - 4lb = (l-b)^2
400 - 384 = (l-b)^2
l-b= 4
l=12 , b=8
as the cyclists go in prependicular directions so we have to use pythagoras to find there distance in form of v
(2v)^2 + (2v+10)^2 = (50)^2 implies v= 15
7) 34= 34 × 1 or 17×2
no other case
17×2 does not satisfy sum of ages condition
therefore answer is 39 and 6
8) let length and breadth be l and b
lb = 96
(l+1)(b+1)=117 implies
lb + l + b +1= 117
l+b = 20,
(l+b)^2 - 4lb = (l-b)^2
400 - 384 = (l-b)^2
l-b= 4
l=12 , b=8
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