A frog is there in the well which 24m deep The frog wants to jump out of the well - Maths - Rational Numbers

Question

A frog is there in the well which 24m deep The frog wants to jump
out of the well Everytime he jumps 2/3m and falls back by 1/4m In
how many jumps will he come out of the well?

Ankush Jain · Accepted Answer

Given, depth of the well = 24m Upward distance covered by frog in one jump = $\frac{2}{3}$ m Downward distance moved when he fall back in one jump = $\frac{1}{4}$ m $∴ total upward distance covered by frog in one second = \frac{2}{3} m - \frac{1}{4} m = \frac{8 m - 3 m}{12} = \frac{5 m}{12}$ $\frac{5}{12}$ m of height required one jump of frog $∴ 24 m of height required = \frac{\frac{1}{5}}{12} \times 24 = \frac{12}{5} \times 24 = \frac{288}{5} = 57 6$ Here the jump comes in decimals which is not possible ${So, in 56}^{th} jump distance covered by frog = \frac{5}{12} \times 56 = \frac{280}{12} m$ Now, in 57th jump first he moves $\frac{2}{3}$ m then he falls back by $\frac{1}{4}$ m $∴ height covered in 57 jump = \frac{280}{12} + \frac{2}{3} = \frac{288}{12} = 24 m$ Hence, in 57th jump, the frog will move out of the well

A frog is there in the well which 24m deep. The frog wants to jump out of the well. Everytime he jumps 2/3m and falls back by 1/4m. In how many jumps will he come out of the well?