A boy was asked to multiply a given number with $$\frac 5{11}$$​. Instead, he divided the same number by $$\frac 5{11}$$​. Thus, his answer exceeded the correct answer by 192. What is the given number?

A number was to be multiplied by$$\frac{5}{11}$$​, but it was divided by $$\frac{5}{11}$$ instead, resulting in an excess of 192.

If a number is divided by a fraction instead of multiplied, the mistaken result differs from the correct result.

Solution: 

Let the number be x.

According to the question;

​$$x \div \frac{5}{11}-x \times \frac{5}{11} = 192 \\ \ \\ \frac{11x}{5 } - \frac{5x}{11} = 192 \\ \ \\ \frac{121x - 25x}{55} = 192 \\ \ \\ 96x = 192 \times 55 \\ \ \\ x = \frac{192 \times 55}{96} \\ \ \\ \implies x = 110$$​​