In the given questions, two quantities are given, one as Quantity I and another as Quantity II. You have to determine relationship between two quantities and choose the appropriate option.
a: If quantity I ≥ quantity II
b: If quantity I > quantity II
c: If quantity I < quantity II
d: If quantity I = quantity II or the relationship cannot be established from the information that is given
e: If quantity quantity II
Arun and Bhadra are brothers. In how many years from now will Bhadra’s age be 50 years ? •
I. The ratio of the current ages of Arun and Bhadra is 5 : 7 respectively.
II. Bhadra was born 10 years before Arun.
III. 5 years hence, Arun’s age would be three-fourth of Bhadra’s age at that time.
I & II : Let Arun's age = $$x$$ years
=> Bhadra's age = $$x + 10$$ years
$$\therefore \frac{x}{x + 10} = \frac{5}{7}$$
=> $$7x = 5x + 50$$
=> $$7x - 5x = 2x = 50$$
=> $$x = \frac{50}{2} = 25$$
=> Bhadra's age = $$25 + 10 = 35$$ years
Thus, I & II are sufficient.
II & III : Let Arun's age = $$x$$ years
=> Bhadra's age = $$x + 10$$ years
$$\therefore \frac{x + 5}{x + 15} = \frac{3}{4}$$
=> $$4x + 20 = 3x + 45$$
=> $$4x - 3x = 45 - 20$$
=> $$x = 25$$
=> Bhadra's age = $$25 + 10 = 35$$ years
Thus, II & III are sufficient.
I & III : Let Arun's age = $$5x$$ years
=> Bhadra's age = $$7x$$ years
$$\therefore \frac{5x + 5}{7x + 5} = \frac{3}{4}$$
=> $$20x + 20 = 21x + 15$$
=> $$21x - 20x = 20 - 15$$
=> $$x = 5$$
=> Bhadra's age = $$7 \times 5 = 35$$ years
Thus, I & III are sufficient.
$$\therefore$$ Any two of the three statements are sufficient.
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