Pair of Linear ...

The sum of the numerator and the denominator of a fraction is equal to $$7$$. Four times the numerator is $$8$$ less than $$5$$ times the denominator. Find the fraction.

$$1250$$ persons went to see a circus-show. Each adult paid Rs. $$75$$ and each child paid Rs. $$25$$ for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to Rs. $$61,250$$.

Rohit says to Ajay "Give me a hundred, I shall then become twice as rich as you." Ajay replies "If you give me ten, I shall be six times as rich as you." How much does each have originally?

The sum of two-digit numbers and the number obtained by reversing the order of the digit is $$121$$. Find the number, if the digits differ by $$3$$.

The pair of linear equations $$2x+5y=k, kx+15y=18$$ has infinitely many solutions if

The pair of equations $$3x+4y=k, 9x+12y=6$$ has infinitely many solutions if

The pair of linear equations $$3x+7y=k, 12x+2ky=4k+1$$ do not have any solution if

If the system of equations
$$3x + y =1$$
$$\left(2k - 1\right)x + \left(k - 1\right)y = 2k + 1$$ is inconsistent, then $$k =$$

The difference between two whole numbers is $$26$$ and one number is three times the other. Find the numbers.

The value of k for which the system of linear equations: $$kx+4y=k-4$$, $$16x+ky=k$$, has infinitely many solutions, is