∆∆∆maths problems for genius∆∆∆
1◆ Find the sum of all 3 digit numbers which are divisible by 4a nd 3
2◆A bicycle wheel makes 75 revolutions per minute to maintain speed 8.19km/hr.Find the diameter of the wheel.
【【50 points ™】】
Answers
1.⬆️
2.
Given that:-
Bicycle wheel makes 75 revolutions per minute.
Speed of wheel = 8.91 km/hr.
Let radius of wheel = r km.
We know that-
Distance covered in one revolution of the wheel = circumference of the wheel.
= 2πr km
∴ Distance covered in one minute = 2π r ×75
= 150π r km.
Hence, Distance covered in one hr = 150π r × 60 km.
By given condition-
Speed of wheel = 8.91 km/hr
or r = 0.315 m [∵ 1 km = 1000 m]
Plz Follow Me ☺️❣️
1.the numbers which are divisible by 4 and 3, is a multiple of 4×3 i.e.
they are multiple of 12.
the lowest 3 digit number which is divisible by 12 is 108.
the largest 3 digit number which is divisible by 12 is 83×12=996 [since 1000/12=83.33]
let the total number of 3 digit numbers which is divisible by 4 and 3 is n.
therefore 996=108+(n-1)×12
906-108=(n-1)×12
888=(n-1)×12
n-1=888/12=74
n=74+1=75
therefore the sum of the numbers which are divisible by 4 and 3 (i.e. divisible by 12) is
=75/2(108+996)
=75/2(1104)
=75×552
=41400
2.Given that:-
Bicycle wheel makes 75 revolutions per minute.
Speed of wheel = 8.91 km/hr.
Let radius of wheel = r km.
We know that-
Distance covered in one revolution of the wheel = circumference of the wheel.
= 2πr km
∴ Distance covered in one minute = 2πr ×75
= 150πr km.
Hence, Distance covered in one hr = 150πr × 60 km.
By given condition-
Speed of wheel = 8.91 km/hr
150πr×60=8.91
r= 8.19×7/150×22×60
r=819=7/150×22×60×100
r=6237/19800000
r=0.000315km
or r = 0.315 m [∵ 1 km = 1000 m]
or r = 31.5 cm [∵ 1 m = 100 cm]
Hence Diameter of wheel = 2 × r
= 2 × 31.5 cm
= 63 cm