One-fifth of a number is equal to $$\dfrac{5}{8}th$$ of another number. If 35 is added to the first number, it becomes four times of the second number. Find the second number.

Let us assume the first number is A and the second number is B.

One-fifth of a number is equal to $$\dfrac{5}{8}th$$ of another number.

$$\dfrac{A}{5}=\dfrac{5B}{8}$$

=> $$A=\dfrac{25B}{8}$$ -----(1)

Also, if 35 is added to the first number, it becomes four times the second number.

$$A+35=4B$$ .......(2)

Substituting the value of (1) in (2)

$$\dfrac{25B}{8}+35=4B$$

$$\dfrac{7B}{8}=35$$

B = 40

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