Question

Choose the correct alternative answers for the following questions.

(i) If 3x + 5y = 9 and 5x + 3y= 7 then What is the value of x + y ?

(A) 2 (B) 16 (C) 9 (D) 7

(ii) 'When 5 is subtracted from length and breadth of the rectangle, the perimeter becomes 26.' What is the mathematical form of the statement ?

(A) x $-$ y = 8 (B) x + y = 8 (C) x + y = 23 (D) 2x + y = 21

(iii) Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age ?

(A) 20 (B) 15 (C) 10 (D) 5

Answer 1

(i) 3x + 5y = 9 .....(I)
5x + 3y= 7 .....(II)
Adding (I) and (II) we have
$$\begin{gathered} 8x+8y=16 \\ \Rightarrow x+y=2 \end{gathered}$$
Hence, the correct answer is option (A).

(ii) Let the length be x and the breadth be y.
Perimeter of the rectangle = 2(l + b) = 26
2(l + b) = 26
$$\begin{gathered} \Rightarrow 2\left[\left(x-5\right)+\left(y-5\right)\right]=26 \\ \Rightarrow 2\left[x+y-10\right]=26 \\ \Rightarrow x+y=23 \end{gathered}$$
Hence, the correct answer is option (C).

(iii) Let Ajay's age be x years and Vijay's age be y years.
Ajay is younger than Vijay by 5 years.
$y-x=5.....\left(\mathrm{I}\right)$
Sum of their ages is 25 years.
$x+y=25.....\left(\mathrm{II}\right)$
Adding (I) and (II) we have
$$\begin{gathered} 2y=30 \\ \Rightarrow y=15 \\ x=10 \end{gathered}$$
Thus, Ajay's age is 10 years.
Hence, the correct answer is option (C).