The diff of 2 nos. is 5 and the diff of their reciprocals is 1/10. Find the nos?

Answer 1

a-b = 5 eq1
1/b-1/a=1/10 eq2

(a-b)/ab = 1/10
a-b=ab/10 eq3

solving eq1&eq3
ab/10=5
ab=50 eq4
a=50/b eq5

substitute eq5 in eq1
50/b -b=5
50-b^2=5b
b^2+5b-50=0 eq6

solving eq6
b=-10 or b=5
so a=-5 or b=10

Ans:
-5, -10
or
10, 5

Answer 2

Let the numbers be x and y. Let x > y

x - y = 5.....(1)
1/y - 1/x = 1/10.....(2)

Consider (2)
1/y - 1/x = 1/10
(x - y)/xy = 1/10
5/xy = 1/10
1/xy = 1/50
xy = 50.....(3)

Consider (1),
x - y = 5
x = 5 + y.....(4)

Substitute (4) in (3)

xy = 50
y(5 + y) = 50
y^2 + 5y = 50
y^2 + 5y - 50 = 0
y^2 - 5y + 10y - 50 = 0
y(y - 5) + 10(y - 5) = 0
(y + 10)(y - 5) = 0

Two possible values of y are -10 and 5
Continue solving. Maybe then one value can be proved as impossible.

Using y = 5 in (1)
x - y = 5
x = 10

Using y = -10 in (1)

x - y = 5
x = -5

When x = 10, y = 5
When x = -5, y = -10

And that's all. There are two possible values for x and y.

Answer 3

Let a and b the two numbers. a - b = Mod 5 (we are ignoring the sign since a may be smaller than b).

1/a - 1/b = 1/10

or b-a / ab = 1/10

b-a X 10 = ab

5 X 10 = 50 = ab

The numbers are 5 and 10.
Check for the answers.

difference = 5 -10 r 10 -5 = 5

1/5 - 1/10 = 2-1/10 = 1/10

So our solution is correct.

Answer 4

Let the two numbers be A and B
so 1st their difference is 5
=> A-B=5 ( eq 1)
= A=5+B
and 2nd their reciprocal would be 1/A and 1/b ,their difference = (1/A)-(1/B)=1/10
= (B-A)/AB=1/10 (taking teir L.C.M)
= 10B-10A=AB
substitute the value of A from eq 1
= 10B-10(B+5)=(B+5)B
= -50=B^2+5B
= B(B+5)=-50
B=-50 or B=-55
substitute this value of B in eq 1
therefore A=-45,-50

Answer 5

Let the numbers be x and y.Let x be the bigger no.

x-y=5........(1)
1/y-1/x=1/10
=>(x-y)/xy=1/10
=>5/xy=1/10
xy=50
now,(x+y)^2
=(x-y)^2+4xy
=(5)^2+4*50
=225
Hence x+y=15....(2)
Solving equations 1 and 2,we get
x=10 and y=5
kTherefore the numbers are 10 and 5

Answer 6

a-b=5

1/b-1/a=1/10 so that
(a-b)/ab=1/10 or ab=50

So
(b+5)b = 50
b² + 5b - 50 = 0
(b+10)(b-5) = 0

If b is 5, then a is 10
If b is -10 then a is -5

Ie. you can have either 5 and 10
or you can have -5 and -10

Answer 7

Let the nos. be x & y. x being the greater no.Then
Two solutions given by the Quadratic eqn. ->
y2-5y-50=0
x=15,y=10
x=0,y= -5.
This 2nd one is not feasible.
So the Answer is the greater number is 15 & smaller one is 10.
Ans : 15,10

Answer 8

let d nos b x nd y, where, x>y
==>x-y=5
==>x=5-y

now,
1/y-1/x=1/10 (1/y>1/x)
(x-y)/xy=1/10
(5)/(5-y)y=1/10
5/5y-y^2=1/10
50=5y-y^2
y^2-5y+50=0
y^2-10y+5y+50=0
(y-10)(y+5)=0
==>y=10 or y= -5
if y=10 then, x=5-10= -5
if y= -5 then, x=5+5=10

therefore, d nos. are 10 nd -5

Answer 9

x-y=5 - 1
1/x+1/y=1/10 - 2
from 1 x=y+5
put value of x in 2

1/y+5 +1/y=1/10

rest u solve

Answer 10

x-y=5
1/x - 1/y = 1/10

Solving both the equations we get

x=10 & y=5