Arithmetic aptitude :: Problems on Ages :: Data Sufficiency 2

• Problems on Ages - General Questions
• Problems on Ages - Data Sufficiency 1
• Problems on Ages - Data Sufficiency 2
• Problems on Ages - Data Sufficiency 3

What is the present age of Divya?
I) The ratio between the present ages of Divya and her brother Arun is 3:4 respectively.
II) After 5 years the ratio between the ages of Divya and Arun will be 4:5.
III) Arun is 5 years older than Divya.

Answer:

Explanation:

I). Let the present ages of Divya and Arun be $3x$ years and $4x$ years.
II). After $5$ years, (Divya's age) : (Arun's age) $= 4:5$.
III). (Arun's age) = (Divya's age) $+5$.

From I and II, we get $\frac{3x+5}{4x+5}$ $=\frac{4}{5}$. This gives $x$.
$\therefore$ Divay's age $=3x$ can be found. Thus, I and II give the answer.

From I and III, we get $4x-3x+5$. This gives x.
$\therefore$ Divay's age $=3x$ can be found. Thus, I and III give the answer.
From III: Let Divya's present age be $t$ years.
Then, Arun's present age $=(t+5)$ years.
Thus, from II and III, we get : $\frac{t}{t+5}$ $=\frac{4}{5}$. This gives $t$.
Thus, II and III give the answer.
$\therefore$ Corrrect answer is (E).

What is Ram's present age?
I) Five years ago, Ram's age was double that of his daughter's age at that time.
II) Present ages of Ram and his daughter are in the ratio of 11:6 respectively.
III) Five years hence, the respective ratio of Ram's age and his daughter's age will become 12:7

Answer:

Explanation:

II). Let the preset ages of Ram and his daughter be $11x$ and $6x$ years respectively.

I) $5$ years ago, Ram's age $= 2 \times$ His daughter's age.

III) $5$ years hence, Ram's age / Daughter's age $=\frac{12}{7} $.
Clearly, any two of the above will give Ram's present age.
$\therefore$ Correct answer is (D).

What is the difference between the ages of A and B?
I) The ratio between the ages of A and B is 2:3
II) B's age is 50% more than A's age.
III) One-fourth of A's age is equal to one-sixth of B's age.

Answer:

Explanation:

I) $A:B=2:3$
$\Rightarrow \frac{A}{B} = \frac{2}{3}$
$\Rightarrow 3A = 2B$.

II) $B=\frac{150}{100}A$
$\Rightarrow B = \frac{3A}{2}$
$\Rightarrow 3A = 2B$.

III) $\frac{1}{4}A$ $=\frac{1}{6}B$
$\Rightarrow 6A = 4B$
$\Rightarrow 3A = 2B$.
Thus, even I, II and II together do not give the answer.
$\therefore$ Correct answer is (E).

What is present age of X?

I) The sum of the ages of X and Y is 21 years.
II) The difference of the ages of X and Y is 5 years.
III) The prduct of the ages of X and Y is 104 years.

Answer:

Explanation:

I) $X+Y=21$
II) $X-Y=5$
III) $XY=104$

Clearly, any two of three statement will give the answer. So, correct answer is (D)

• Problems on Ages - General Questions
• Problems on Ages - Data Sufficiency 1
• Problems on Ages - Data Sufficiency 2
• Problems on Ages - Data Sufficiency 3