Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question. The difference between father's age and son's age is 21 years now. What is the present age of the son?
Statements
I. After five years, the ratio of father's age to that of the son would be 5:2.
II. The sum of father's age and son's age after five years would be 66 years.
Let F represent the father's current age and S represent the son's current age.
From the problem statement, we know the difference between their ages:
$F - S = 21$ (Equation 1)
Statement I Sufficiency Analysis
Statement I provides the ratio of their ages after five years:
Father's age after 5 years = $F + 5$
Son's age after 5 years = $S + 5$
Ratio: $\frac{F + 5}{S + 5} = \frac{5}{2}$
Cross-multiplying gives:
$2(F + 5) = 5(S + 5)$
$2F + 10 = 5S + 25$
$2F - 5S = 15$ (Equation 2)
Now we have a system of two linear equations:
- $F - S = 21 \implies F = S + 21$
- $2F - 5S = 15$
Substitute $F = S + 21$ into the second equation:
$2(S + 21) - 5S = 15$
$2S + 42 - 5S = 15$
$-3S = 15 - 42$
$-3S = -27$
$S = 9$
Statement I alone is sufficient to find the son's present age, which is 9 years.
Statement II Sufficiency Analysis
Statement II provides the sum of their ages after five years:
Father's age after 5 years = $F + 5$
Son's age after 5 years = $S + 5$
Sum: $(F + 5) + (S + 5) = 66$
$F + S + 10 = 66$
$F + S = 56$ (Equation 3)
Now we have another system of two linear equations:
- $F - S = 21$ (Equation 1)
- $F + S = 56$ (Equation 3)
Add Equation 1 and Equation 3:
$(F - S) + (F + S) = 21 + 56$
$2F = 77$
$F = 38.5$
Substitute $F = 38.5$ into Equation 3:
$38.5 + S = 56$
$S = 56 - 38.5$
$S = 17.5$
Statement II alone is sufficient to find the son's present age, which is 17.5 years.
Conclusion on Statement Sufficiency
Since both Statement I and Statement II individually provide enough information to calculate the son's present age, either statement alone is sufficient.
Important Questions from Data Sufficiency (Notes)
- In light of the statements I and II choose the most appropriate option.
If a group comprises of five persons A, B, C, D and E, then how many persons are taller than E?
Statement (I) A is taller than B and B is shorter than A and E only.
Statement (II) C is shorter than A and A is shorter than E. - In light of the statements I and II choose the most appropriate option.
Eight boxes- A, B, C, D, P, Q, R and S are stacked vertically but not necessarily in the same order. Which among them is kept immediately above R?
Statement (I) Only three boxes are kept above D and only one box is kept between D and Q. Q is kept lower than D and is immediately below P.
Statement (II) Only one box is kept between A and C. C is kept three boxes above Q. As many boxes are kept above B as are kept below R. A question along with a set of statements is given below. We have to find which of the given statements is/are sufficient to answer the given question.
Question : Find the area of the triangle PQR.
Statements :
I. PQ = 5 m., PR = 5 m.
II. Length of PO is 4 m.P and Q are children of S. Who is the father of P? To answer this question which of the statements (1) and (2) is/are necessary?
(1) R is the brother of P and the son of T.
(2) U is the mother of Q.Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question.
Question:
Rajesh's salary is Rs. 12,500. What is Arvind's salary?
Statements
I. Arvind gets $\frac{3}{5}$th of the total salary of his and Rajesh'
II. Two-thirds of Arvind's salary is equal to the average salary of both.
