Solve the equation: $\frac{x + 3}{x + 2} - \frac{x - 4}{x + 3} = \frac{x + 5}{x + 4} - \frac{x + 6}{x + 5}$

Created: 3 months ago | Updated: 2 months ago

Job Solution One Bank Ltd ONE Bank Ltd. || SCO Examination (29-06-2018) || 2018 গণিত

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$\frac{x + 3}{x + 2} - \frac{x + 4}{x + 3} = \frac{x + 5}{x + 4} - \frac{x + 6}{x + 5} \Rightarrow \frac{x + 2 + 1}{x + 2} + \frac{1}{x + 2} - \frac{x + 3}{x + 3} - \frac{1}{x + 3} = \frac{x + 4 + 1}{x + 4} + \frac{x + 5 + 1}{x + 5} \Rightarrow \frac{x + 2}{x + 2} + \frac{1}{x + 2} - \frac{x + 3}{x + 3} - \frac{1}{x + 3} = \frac{x + 4}{x + 4} + \frac{1}{x + 4} - \frac{x + 5}{x + 5} - \frac{1}{x + 3} \Rightarrow 1 + \frac{1}{x + 2} - 1 - \frac{1}{x + 3} = 1 + \frac{1}{x + 4} - 1 - \frac{1}{x + 5} \Rightarrow \frac{1}{x + 2} - \frac{1}{x + 3} = \frac{1}{x + 4} - \frac{1}{x + 5} \Rightarrow \frac{x + 3 - (x + 2)}{(x + 2) (x + 3)} = \frac{x + 5 - (x + 4)}{(x + 4) (x + 5)} \Rightarrow \frac{x + 3 - x - 2}{(x + 2) (x + 3)} = \frac{x + 5 - x - 4}{(x + 4) (x + 5)} \Rightarrow \frac{1}{(x + 2) (x + 3)} = \frac{1}{(x + 4) (x + 5)} \Rightarrow (x + 4) (x + 5) = (x + 2) (x + 3) \Rightarrow x^{2} + 5 x + 4 x + 20 = x^{2} + 3 x + 2 x + 6 \Rightarrow x^{2} + 9 x - x^{2} - 5 x = 6 - 20 \Rightarrow 4 x = - 14 ∴ x = \frac{- 14}{4} = \frac{- 7}{2}$

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Two men and three women completed only one fourth portion of a job in 3 days. After 3 days, another man was included in the team and two days they completed another one fourth portion of the job. How many men (with no women) can complete the whole job in 4 days?

Created: 3 months ago | Updated: 2 months ago

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Two men and three women completed only one fourth portion of a job in 3 days. After 3 days, another man was included in the team and two days they completed another one fourth portion of the job. How many men (with no women) can complete the whole job in 4 days?

A sum of money is to be distributed equally among a group of children. If there were 25 children less then each would get Tk. 1.50 more, and if there were 50 children more, each would get Tk. 1.50 less. Find the number of children and the amount of money distributed.

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Solve the equation: $\frac{x + 3}{x + 2} - \frac{x - 4}{x + 3} = \frac{x + 5}{x + 4} - \frac{x + 6}{x + 5}$