Laxmi's father is 51 years old. He is three years older than three times Laxmi's age. The age of Laxmi is :

If $2^{(x+y)} = 64$ and $128^{(x-y)} = 2$, then what is the value of x?

The present age of a father is 4 years more than double the age of his son. After 10 years, the father's age is 30 years more than his son. Then the present age of father is:

If on dividing 26 into two parts, we find that three times the first and seven times the second part together equals to 122. Then, the ratio of first and second part shall be:

Which of the following pair of linear equations has / have many infinite solutions?

A. $9x + 3y + 12 = 0$; and $18x + 6y + 24 = 0$

B. $2x - 3y = 13$; and $7x - 2y = 20$

C. $x + y = 5$; and $2x + 2y = 10$

D. $3x + y - 3 = 0$; and $2x + \dfrac{2}{3}y = 2$

Choose the correct answer from the options given below:

Read the information given below carefully and answer the question that follows:

Aditi, a salesgirl is appointed at a basic salary of ₹ 1200 per month. The condition of employment further stated that for every sale of ₹ 10000 or above she does, she will get 50 % of basic salary and 10 % of the sales as special incentive. However, this incentive scheme shall not work on the first ₹ 10000 of sales made. What should be the value of sales if Aditi wants to earn ₹ 7600 in a particular month?

For what value of k, the system of equations $3x - ky - 3 = 0$ and $2x - 3y - 4 = 0$ has no solution?