Ajay and Manoj had certain amounts of Money with them.The ratio of the amounts with them is 8:5. Each day Ajay spends a certain amount and Manoj earns one sixth of the amount that Ajay spends.after 9 days,the ratio of the amounts with them is 10:11.After how many more days,will the ratio of the ratio of the amount with them be 18:35?

Hi Arti, Answer is 3 days. Lets consider the initial amounts with them to be 8x and 5x Lets say Ajay spends an amount a everyday, then we have $$\frac{\left(8x-9a\right)}{5x+\frac{9a}{6}}=\frac{10}{11}\ \longrightarrow \ \ 3a=x$$ Lets say that a ratio of 18:35 is reached after n days we have $$\frac{\left(8x-na\right)}{5x+\frac{na}{6}}=\frac{18}{35}$$ Substituting $$x=\frac{a}{3}\ $$, we get $$\frac{\left(144x-6nx\right)}{90x+nx}=\frac{18}{35}\longrightarrow \ \longrightarrow \ \longrightarrow \ n=15$$ Hope this helps:)

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