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There are 1400 students and 50 teachers in a school. For a charity work, each student and teacher donated money, such that the money donated by all the teachers is 12.5% of the total money collected, while the money donated by 320 students is 20% of the total money collected. If a teacher donated Rs. 60 more than a student, then how much total money was collected by the school?

There are 1400 students and 50 teachers in a school. For a charity work, each student and teacher donated money, such that the money donated by all the teachers is 12.5% of the total money collected, while the money donated by 320 students is 20% of the total money collected. If a teacher donated Rs. 60 more than a student, then how much total money was collected by the school? Correct Answer Rs. 32000

Let each student donated Rs. ‘x’ for the charity work

⇒ Each teacher donated = Rs. (x + 60)

Now,

Money donated by all teachers = 50 × (x + 60)

⇒ 12.5% of Total money collected = 50x + 3000

⇒ 1/8 × Total money collected = 50x + 3000

⇒ Total money collected = 400x + 24000       ---- (1)

Also,

Money donated by 320 students = 320x

⇒ 20% of Total money collected = 320x

⇒ 1/5 × Total money collected = 320x

⇒ Total money collected = 1600x       ----(2)

Equating (1) and (2),

⇒ 1600x = 400x + 24000

⇒ 1200x = 24000

⇒ x = Rs. 20

Substituting in (2),

∴ Total money collected by school = 1600 × 20 = Rs. 32000

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