A, B and C have a few coins with them. 7 times the number of coins that A has is equal to 5 times the number of coins B has while 8 times the number of coins B has is equal to 13 times the number of coins C has. What is the minimum number of coins with A, B and C put together?a)100b)280c)212d)156Correct answer is option 'C'. Can you explain this answer?

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A, B and C have a few coins with them. 7 times the number of coins that A has is equal to 5 times the number of coins B has while 8 times the number of coins B has is equal to 13 times the number of coins C has. What is the minimum number of coins with A, B and C put together?

a)
100
b)
280
c)
212
d)
156

Correct answer is option 'C'. Can you explain this answer?

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A, B and C have a few coins with them. 7 times the number of coins tha...

So, final ratio of [A:B:C :: (5 x 13) : (7 x 13) : (8 x 7)]
minimum number of coins is equal to sum of their ratio = (65 + 91 + 56) = 212

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A, B and C have a few coins with them. 7 times the number of coins tha...

Let's solve the problem step by step:

Step 1: Convert the given information into equations
- 7 times the number of coins that A has is equal to 5 times the number of coins that B has: 7A = 5B
- 8 times the number of coins that B has is equal to 13 times the number of coins that C has: 8B = 13C

Step 2: Simplify the equations
- We can divide both sides of the first equation by 7 to get A = (5/7)B
- We can divide both sides of the second equation by 8 to get B = (13/8)C

Step 3: Substitute the value of B from the second equation into the first equation
- Substituting (13/8)C for B in the first equation, we get A = (5/7)(13/8)C
- Simplifying this equation, we have A = (65/56)C

Step 4: Find the minimum number of coins
- To find the minimum number of coins, we need to find the lowest common multiple (LCM) of the coefficients of C, which are 56 and 8.
- The LCM of 56 and 8 is 56, so C must be a multiple of 56.
- Let's take the smallest possible value for C, which is 56.
- Substituting C = 56 into the equation A = (65/56)C, we get A = (65/56)(56) = 65

Step 5: Calculate the total number of coins
- Now that we know A = 65, we can substitute this value back into the equation B = (13/8)C to find B.
- B = (13/8)(56) = 91
- The total number of coins is A + B + C = 65 + 91 + 56 = 212

Therefore, the minimum number of coins with A, B, and C put together is 212, which corresponds to option C.

Answered by Notes Wala · View profile

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