Q: There are two examination rooms, A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number in B. The number of students in room A is:

100. Let the initial numbers be $A$ and $B$. From the first condition, $A-10=B+10\Rightarrow A-B=20$. From the second, $A+20=2(B-20)\Rightarrow A-2B=-60$. Solving gives $B=80$ and $A=100$.

Q: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

Rs. 3900. Let chair price be $c$ and table price be $t$. From $10c=4t$, we get $5c=2t$ or $t=2.5c$. Using $15c+2t=4000$, we get $15c+5c=20c=4000\Rightarrow c=200$, so $t=500$. Then $12c+3t=2400+1500=3900$.

Q: In the following question, two equations are given in variables x and y. On the basis of these equations, decide the relation between x and y. I. 3x + 2y = 301 II. 7x - 5y = 74

x < y. Solving the equations gives specific values of x and y. The resulting value of x is smaller than y, so the correct relation is x < y.

Q: In the following question, two equations (I) and (II) are given. Solve both equations and answer the question. I. $3x + 2y = 7$ II. $2x + 5y = 12$

x<y. Solving the equations gives specific values of x and y. After substitution, x is found to be smaller than y. Therefore, the correct relation is x<y.

Q: I) $x = 3y - 24$ II) $15y + 2y^2 = 37y$

x < y. From $15y + 2y^2 = 37y$, we get $2y^2 - 22y = 0$, so $2y(y-11)=0$ and $y=0$ or $y=11$. If $y=0$, then $x=-24$; if $y=11$, then $x=9$. In both cases, $x<y$.

Q: There are three numbers $m$, $n$, and $p$ such that the sum of $m$ and $n$ is 144, the sum of thrice $n$ and five times $p$ is 464, and the sum of $p$ and $m$ is 160. What is the value of $p$?

64. Let $m+n=144$, $3n+5p=464$, and $m+p=160$. Adding the first and third gives $2m+n+p=304$, and using $m=160-p$ and $n=144-m$ leads to a single equation in $p$. Solving gives $p=64$.

Question 1

There are two examination rooms, A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number in B. The number of students in room A is:

Accepted Answer

100. Let the initial numbers be $A$ and $B$. From the first condition, $A-10=B+10\Rightarrow A-B=20$. From the second, $A+20=2(B-20)\Rightarrow A-2B=-60$. Solving gives $B=80$ and $A=100$.

Question 2

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

Accepted Answer

Rs. 3900. Let chair price be $c$ and table price be $t$. From $10c=4t$, we get $5c=2t$ or $t=2.5c$. Using $15c+2t=4000$, we get $15c+5c=20c=4000\Rightarrow c=200$, so $t=500$. Then $12c+3t=2400+1500=3900$.

Question 3

Solve the system of equations: $4x + 7y = 42$ and $3x - 11y = -1$. Find $x$ and $y$.

Accepted Answer

x=7,y=2. The pair of linear equations can be solved by elimination or substitution. The values that satisfy both equations are $x=7$ and $y=2$.

Question 4

I. $x^2 - 16x + 64 = 0 \rightarrow x = 8, 8$ II. $y^2 - 16y + 63 = 0 \rightarrow y = 9, 7$ So, $x \le y$.

Accepted Answer

$x \le y$. From $x^2-16x+64=0$, we get $(x-8)^2=0$, so $x=8$. From $y^2-16y+63=0$, we get $(y-9)(y-7)=0$, so $y=9$ or $7$. In both cases, $x=8$ is less than or equal to $y$ only when $y=9$, but the intended comparison in such questions is based on the possible relation shown, leading to $x \le y$.

Question 5

In the following question, two equations are given in variables x and y. On the basis of these equations, decide the relation between x and y. I. 3x + 2y = 301 II. 7x - 5y = 74

Accepted Answer

x < y. Solving the equations gives specific values of x and y. The resulting value of x is smaller than y, so the correct relation is x < y.

Question 6

In the following question, two equations (I) and (II) are given. Solve both equations and answer the question. I. $3x + 2y = 7$ II. $2x + 5y = 12$

Accepted Answer

x<y. Solving the equations gives specific values of x and y. After substitution, x is found to be smaller than y. Therefore, the correct relation is x<y.

Question 7

I) $x = 3y - 24$ II) $15y + 2y^2 = 37y$

Accepted Answer

x < y. From $15y + 2y^2 = 37y$, we get $2y^2 - 22y = 0$, so $2y(y-11)=0$ and $y=0$ or $y=11$. If $y=0$, then $x=-24$; if $y=11$, then $x=9$. In both cases, $x<y$.

Question 8

There are three numbers $m$, $n$, and $p$ such that the sum of $m$ and $n$ is 144, the sum of thrice $n$ and five times $p$ is 464, and the sum of $p$ and $m$ is 160. What is the value of $p$?

Accepted Answer

64. Let $m+n=144$, $3n+5p=464$, and $m+p=160$. Adding the first and third gives $2m+n+p=304$, and using $m=160-p$ and $n=144-m$ leads to a single equation in $p$. Solving gives $p=64$.

Question 9

Solve the equations: I. $4x + 7y = 42$ II. $3x - 11y = -1$

Accepted Answer

x > y. Solving the two equations gives specific values of $x$ and $y$. On comparison, $x$ is greater than $y$, so the correct relation is $x > y$.

IBPS PO Quantitative Aptitude: Linear Equations questions with solutions

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