Question

Mark the correct alternative in the following question:

If the sum of a number and its two-fifth is 70. The number is

(a) 70 (b) 50 (c) 60 (d) 90

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}x. \\ \mathrm{As},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{a}\mathrm{number}\mathrm{and}\mathrm{its}\mathrm{two}-\mathrm{fifth}\mathrm{is}70. \\ \Rightarrow x+\frac{2}{5}x=70 \\ \Rightarrow \frac{x}{1}+\frac{2x}{5}=70 \\ \Rightarrow \frac{5x}{5}+\frac{2x}{5}=70 \\ \Rightarrow \frac{5x+2x}{5}=70 \\ \Rightarrow \frac{7x}{5}=70 \\ \Rightarrow 7x=70\times 5\left(\mathrm{By}\mathrm{transposing}5\mathrm{to}\mathrm{RHS}\right) \\ \Rightarrow 7x=350 \\ \Rightarrow x=\frac{350}{7}\left(\mathrm{By}\mathrm{transposing}7\mathrm{to}\mathrm{RHS}\right) \\ \therefore x=50 \end{gathered}$$

So, the number is 50.

Hence, the correct alternative is option (b).