The sum of the two numbers is 15 and the sum of their reciprocals is 3/10.Find the numbers.
Vikas TU , 14 Years ago
Grade 12th Pass
Magical Mathematics[Interesting Approach]> Linear equations...
3 AnswersTejas Paresh Lodaya
Last Activity: 14 Years ago
x+y=15
y+x/xy=3/10
1/x + 1/15-x=3/10
150=45x-3x2
3x2-45x-150=0
x2-15-50=0
Therefore no.are 5 and 10
Sudheesh Singanamalla
Last Activity: 14 Years ago
let the numbers be x and y
so
x+y = 15 -------------------------(i)
and 1/x + 1/y = 3/10
==> (y + x)/xy = 3/10 (putting (i))
15/ xy = 3/10
5/xy = 1/10
xy = 50 --------------------(ii)
x = 50/y -----------------------(iii)
50/y + y = 15
50 + y2 = 15y
y2 - 15y + 50 = 0
(y-10)(y-5) = 0
y = 10 and y = 5
now there will be 2 numbers for 'x'
substituting y as 10 we get
x = 5 ;
substituting y as 5 we get
x = 10;
so the numbers are x = 10 and y = 5 and viceversa !
PLEASE APPROVE !
Neer Varshney
Last Activity: 14 Years ago
let the numbers be x & y.
x+y=15............1
1/x + 1/y = 3/10...........2
y+x /xy = 3.10
10(x+y)= 3xy.
10(15)= 3(15-y)y.
50 = 15y-y2.
y2-15y+50 = 0.
y2-10y-5y+50 = 0.
y(y-10)-5(y-10)=0.
(y-5)(y-10)=0.
y = 5 or 10.
Similarly x = 10 or 5.
The numbers are 5 and 10.
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on magical mathematics[interesting approach]
Given that (1+5x)⁴ = 1 + Px + Qx² + Rx³ +..... Find the values of P - 2Q + 3R
magical mathematics[interesting approach]
1 Answer Available
Last Activity: 2 Years ago
9 men and 15 boys working 10 hours a day can make 12 pillars in 42 days, in how many days will 12 men and 22 boys working 8 hours a day can make pillars 4 times the previous number?
magical mathematics[interesting approach]
1 Answer Available
Last Activity: 2 Years ago
In the given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter, find angle PCA + angle BCQ?
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 2 Years ago
for any two sets A and B (A-B)U(B-A)U (A intersection B)
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 2 Years ago
If someone has got 150 out of 200 marks in term 1 exam and 160 out of 200 marks in term 2 exam then what is the percentage in30:70
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 3 Years ago