Question

One says, “ give me hundred, friend! I shall then become twice as rich as you.” The other replies, “If you give me ten, I shall become six times as rich as you.” Tell me what is the amount of their respective capital ?

Answer 1

Hint: Try to make equations from the sentences said by the friends. Use two different variables to do that. Two equations must be formed. We will get the required solution by solving these equations.

Complete step-by-step answer:
Let the capital amount of the first friend be x and the capital amount of the second friend be y.
From the statement, said by first friend we make the equation:
(x + 100 = 2y)……. Equation(1)
From the statement, said by second friend we make the equation:
(y + 10 = 6x)……… Equation(2)
Now, Solving the above two equations using substitution method:
Substituting the value of x = (2y - 100) from equation(1) in equation(2), we get
y + 10 = 6(2y – 100)
y + 10 = 12y – 600
Solving,
11y = 610
$y = \dfrac{{610}}{{11}}$ units (Since the currency is not mentioned we prefer writing units)
Putting this value of y in equation(1):
x + 100 = 2$ \times \dfrac{{610}}{{11}}$
solving,
x= $\dfrac{{120}}{{11}}$ units
So the first friend has $\dfrac{{120}}{{11}}$ units capital.
And the second friend has $\dfrac{{610}}{{11}}$ units capital.

Note: In questions like these, use the concept of linear equations in 2 variables. The statements given in the question should be read carefully, to make the correct equations. The equations so formed can be solved by any method- substitution, elimination, cross multiplication etc.