Q9 of 40 Page 86

In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.

Let the number no. of students be x

Let the number no. of benches be y


According to given condition, we have


x = 3y + 1 ⇒ x-3y = 1 …..I


x = 4(y-1) ⇒ x = 4y-4 ⇒ x-4y = -4 ….II


Equating eq. I and II


x-3y = 1


-x + 4y = 4


y = 5


Substituting y = 5 in eq. I


x-3×5 = 1


⇒ x-15 + 1 ⇒x = 16


Number of students = 16;


Number of benches = 5


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