Mathematics
There are two examination halls A and B. If 12 pupils are sent from A to B, the number of pupils in each room becomes the same. If 11 pupils are sent from B to A, then the number of pupils in A is double their number in B. Find the number of pupils in each room.
Linear Equations
1 Like
Answer
Let x and y be the initial number of pupils in examination hall A and B respectively.
Given,
If 12 pupils are sent from A to B, the number of pupils in each room becomes the same.
⇒ x - 12 = y + 12
⇒ x = y + 12 + 12
⇒ x = 24 + y …..(1)
Given,
If 11 pupils are sent from B to A, then the number of pupils in A is double their number in B.
⇒ x + 11 = 2(y - 11)
⇒ x + 11 = 2y - 22
⇒ x - 2y = -22 - 11
⇒ x - 2y = -33 ……..(2)
Substituting value of x from equation (1) in (2), we get :
⇒ 24 + y - 2y = -33
⇒ 24 - y = -33
⇒ y = 24 + 33
⇒ y = 57.
Substituting value of y in equation (1), we get :
⇒ x = 24 + y
⇒ x = 24 + 57
⇒ x = 81.
Hence, no. of pupils in examination hall A = 81 and examination hall B = 57.
Answered By
2 Likes
Related Questions
The monthly incomes of A and B are in the ratio 7 : 5 and their expenditures are in the ratio 3 : 2. If each saves ₹ 1500 per month, find their monthly incomes.
A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Find the quantity of each the solutions to get the resultant mixture.
A and B each have a certain number of marbles. A says to B, “If you give 30 to me, I will have twice as many as left with you.” B replies, “If you give me 10, I will have thrice as many as left with you.” How many marbles does each have?
The present age of a man is 3 years more than three times the age of his son. Three years hence, the man’s age will be 10 years more than twice the age of his son. Determine their present ages.