maths (1 Viewer)

[super.muppy]

a certain integer is between 10 and 100. its value is 8 times the sum of its digits, and if its is reduced by 45, its digits are reversed. Find the integers.

Two ppl are 16 Km apart, they both walk towards each other starting at the same time, after 2 hrs of walking the both meet each other. However if they walk in the same direction (so that the distance between them is gradually decreasing) they will meet in 8 hrs. find both of their speeds.

Thanks heaps in advance

 

[ninetypercent]

a certain integer is between 10 and 100. its value is 8 times the sum of its digits, and if its is reduced by 45, its digits are reversed. Find the integers.

condition one: the digit must be a two digit number.

the digit is 10n + m [1]

Condition two: 8 times the sum of it's digits

10n + m = 8(m + n) [2]

equate [1] and [2]

10n + m = 8m + 8n
-7m = -2n
7m = 2n
n = 7m/2 [3]

condition three : if reduced by 45, digits are reversed

10n + m - 45 = 10m + n [4]
9n - 9m = 45

substitute [3] in [4] for n

9(7m/2) - 9m = 45
31.5m - 9m = 45
22.5m = 45
m = 2

substitute m = 2 in [3]
n = 7x2/2
= 7

The digit is 10n + m
= 10 x 7 + 2
= 72

Hope that made sense

 

[super.muppy]

thanks man wohs with ur level of logic physics or engineering wud have been a breeze for u
thanks again

question 2 anyone? LOL

 

[ninetypercent]

Two ppl are 16 Km apart, they both walk towards each other starting at the same time, after 2 hrs of walking the both meet each other. However if they walk in the same direction (so that the distance between them is gradually decreasing) they will meet in 8 hrs. find both of their speeds.

Let the speed of the faster person 'A' be: x km/h
distance travelled in 2 hours: 2x km
let the speed of the slower person 'B' by y km/h
distance travelled in 2 hours: 2y km

Since they meet, 2x + 2y = 16 [1]
From [1]
x + y = 8 [2]

But suppose they travelled in the same direction.. say 'A' follows 'B'

in 8 hours, A travells 8x km
in 8 hours, B travells 8y km

the extra bit B travels is 8y
A travels 16 km and the extra bit of B
so A travells 16 + 8y in 8 hours

A's speed is (16 + 8y)/8
x= 2 + y [3]

substitute [3] in [2] for x
2 + y + y = 8
2 + 2y = 8
2y = 6
y = 3

substitute y = 3 in [1]
x + y = 8
x + 3 = 8
x = 5

A's speed is 5 km/h
B's speed is 3km/h

 

[ninetypercent]

thanks man wohs with ur level of logic physics or engineering wud have been a breeze for u
thanks again

question 2 anyone? LOL

I don't do physics or engineering. The only maths based course I do is Maths, lol.