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?

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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:)