An oil merchant has 3 varieties of oil of volumes 432, 594 and 702 respectively. The number of cans of equal size that would be required to fill the oil separately is:
a) 25
(b) 24
(c) 22
(d) 26
SSC CPO 13 March 2019 (Evening)
Answer: 8, 11, 13
To solve this problem, we need to find the greatest common divisor (GCD) of the three volumes. The GCD of a set of numbers is the largest number that divides all of them without leaving a remainder. The number of cans of equal size that would be required to fill the oil separately is the volume of each type of oil divided by the GCD.
Here are the steps to solve the problem:
1. First, we need to find the GCD of the three volumes. We can use the Euclidean algorithm to find the GCD of two numbers, and then use the result to find the GCD with the third number.
2. Let's start with the first two volumes, 432 and 594. Using the Euclidean algorithm, we subtract the smaller number from the larger number, and then replace the larger number with the result. We repeat this process until we get a remainder of 0.
3. Subtract 432 from 594 to get 162. Replace 594 with 162 and repeat the process. Subtract 162 from 432 to get 270. Replace 432 with 270 and repeat. Subtract 162 from 270 to get 108. Replace 270 with 108 and repeat. Subtract 108 from 162 to get 54. Replace 162 with 54 and repeat. Subtract 54 from 108 to get 54. Replace 108 with 54 and repeat. Subtract 54 from 54 to get 0. So, the GCD of 432 and 594 is 54.
4. Now, we need to find the GCD of 54 and the third volume, 702. Repeat the same process. Subtract 54 from 702 to get 648. Replace 702 with 648 and repeat. Subtract 54 from 648 to get 594. Replace 648 with 594 and repeat. Subtract 54 from 594 to get 540. Replace 594 with 540 and repeat. Subtract 54 from 540 to get 486. Replace 540 with 486 and repeat. Subtract 54 from 486 to get 432. Replace 486 with 432 and repeat. Subtract 54 from 432 to get 378. Replace 432 with 378 and repeat. Subtract 54 from 378 to get 324. Replace 378 with 324 and repeat. Subtract 54 from 324 to get 270. Replace 324 with 270 and repeat. Subtract 54 from 270 to get 216. Replace 270 with 216 and repeat. Subtract 54 from 216 to get 162. Replace 216 with 162 and repeat. Subtract 54 from 162 to get 108. Replace 162 with 108 and repeat. Subtract 54 from 108 to get 54. Replace 108 with 54 and repeat. Subtract 54 from 54 to get 0. So, the GCD of 54 and 702 is 54.
5. Therefore, the GCD of the three volumes is 54.
6. To find the number of cans of equal size that would be required to fill the oil separately, divide the volume of each type of oil by the GCD. For the first type of oil, 432 divided by 54 is 8. For the second type of oil, 594 divided by 54 is 11. For the third type of oil, 702 divided by 54 is 13.
So, the oil merchant would need 8 cans for the first type of oil, 11 cans for the second type of oil, and 13 cans for the third type of oil.
Answer: 8, 11, 13
.png)
