The students of a school are made to stand in rows. If the number of students in each row is increased by 6, there would be 4 row less. If the number of students in each rows is reduced by 6, there would be 5 rows more. Find the number of students in the school.
Answer:
2160
- Let us assume that there are x students in each row and y rows in total.
Thus, the total number of students in the school is xy. -
If the number of students in each row is increased by 6, then the number of rows becomes (y−4).
As the total number of students remain same, we have xy=(x+6)(y−4)⟹xy=xy−4x+6y−24[ Cancelling xy ]⟹4x−6y=−24…(i) - If the number of students in each row is reduced by 6, then the number of rows becomes (y+5). ∴xy=(x−6)(y+5)⟹xy=xy+5x−6y−30[ Cancelling xy ]⟹−5x+6y=−30…(ii)
- Adding eq(i) and eq(ii), we get ⟹(4−5)x=(−24−30)⟹−x=−54⟹x=54
- Substituting the value of x in eq(i), we get 4×54−6y=−24⟹−6y=−24−216⟹−6y=−240⟹y=40
- Therefore, the total number of students in the school = xy = 54 × 40 = 2160.