Our school decided to award prizes to grade 8 students on the eve ofGandhi jayanthi to inculcate three values -Discipline, Cleanliness andRegularity in attendance. The number of students getting prizes in thethree categories are in the ratio 2 : 3 : 4 and the product of the ratios is192.(i) Find the number of students getting prizes of each value?(ii) If the value of each prize is Rs 200, then find the total amount ofprizes?(iii) Find the least number to be multiplied with 192 , so that it will beperfect cube?(iv) If total students are 360, Find the number of students getting prizesin Discipline?(v) If the value of each prize is Rs 200, then find the total amount ofprizes related to”Regularity in attendance” ?---X----
Question
Our school decided to award prizes to grade 8 students on the eve ofGandhi jayanthi to inculcate three values -Discipline, Cleanliness andRegularity in attendance. The number of students getting prizes in thethree categories are in the ratio 2 : 3 : 4 and the product of the ratios is192.(i) Find the number of students getting prizes of each value?(ii) If the value of each prize is Rs 200, then find the total amount ofprizes?(iii) Find the least number to be multiplied with 192 , so that it will beperfect cube?(iv) If total students are 360, Find the number of students getting prizesin Discipline?(v) If the value of each prize is Rs 200, then find the total amount ofprizes related to”Regularity in attendance” ?---X----
Solution
(i) The ratio of students getting prizes in the three categories is 2:3:4. The product of the ratios is 192. This means that 2x * 3x * 4x = 192, where x is the common multiplier. Solving for x, we get x = 4. Therefore, the number of students getting prizes in each category is 2x = 8 (Discipline), 3x = 12 (Cleanliness), and 4x = 16 (Regularity in attendance).
(ii) The total number of prizes is 8 + 12 + 16 = 36. If each prize is worth Rs 200, then the total amount of prizes is 36 * 200 = Rs 7200.
(iii) To make 192 a perfect cube, we need to multiply it by the least number that will make its prime factors all have multiples of 3. The prime factorization of 192 is 2^6 * 3. Therefore, the least number to multiply with 192 to make it a perfect cube is 3^2 = 9.
(iv) If the total number of students is 360, and the ratio of students getting prizes in Discipline is 2 out of a total ratio of 2 + 3 + 4 = 9, then the number of students getting prizes in Discipline is (2/9) * 360 = 80.
(v) If the number of students getting prizes for Regularity in attendance is 16, and each prize is worth Rs 200, then the total amount of prizes related to Regularity in attendance is 16 * 200 = Rs 3200.
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