Question

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Answer 1

$\large\bf\underline {Question:-}$

To do the same amount of work Raju takes 6 hours less than Joseph. If both together complete the same amount of work in 13 hours 20 minutes find how much time Joseph will takes to complete the work.

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$\large\bf\underline {Given:-}$

• Raju takes 6 hours less than Joseph.
• both together complete the same amount of work in 13 hours 20 minutes.

$\large\bf\underline {To \: find:-}$

• work done by Joseph.

$\huge\bf\underline{Solution:-}$

Let Joseph takes x hours to complete the work.

So, Raju takes ( x-6 ) Hours to complete the work.

Work done by Joseph in 1 hour = 1/x

work done by Raju in 1 hour = 1/x-6

Both complete the same amount of work in 13 hours 20 minutes. So work done by both = 13 + 20/60 = 780+20/60 = 40/3hours.

and work done by both in 1 hour = 3/40

$\rm \mapsto \: \frac{1}{x} + \frac{1}{x - 6} = \frac{3}{40} \\ \\ \rm \mapsto \: \frac{x + x - 6}{x(x - 6)} = \frac{3}{40} \\ \\ \rm \mapsto \: \frac{2x - 6}{x(x - 6)} = \frac{3}{40}$

By cross multiplication:-

$\rm \mapsto \: 40(2x - 6) = 3x(x - 6) \\ \\ \rm \mapsto \: 80x - 240 = 3 {x}^{2} - 18x \\ \\ \rm \mapsto \: 3 {x}^{2} - 98x + 240 = 0 \\ \\ \rm \mapsto \: 3 {x}^{2} - 90x - 8x + 240 \\ \\ \rm \mapsto \: 3x(x - 30) - 8(x - 30) \\ \\ \rm \mapsto \: (3x - 8)(x - 30) \\ \\ \bf \mapsto \: x = \frac{8}{3} \: or \: x = 30$

So we will take x = 30

Then, Time taken Joseph = 30hours

Answer 2

Answer:

Basics. The present perfect tense refers to an action or state that either occurred at an indefinite time in the past (e.g., we have talked before) or began in the past and continued to the present time (e.g., he has grown impatient over the last hour). This tense is formed by have/has + the past participle.