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When 40% of a number E is added to another number R, B becomes 125% of its previous value. Then which of the following is true regarding the values of E and R?
- a)Either (a) or (b) can be true depending upon the values of E and R
- b)R > E
- c)E > R
- d)R = E
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
When 40% of a number E is added to another number R, B becomes 125% of...
R + 40% of E = 125% of R 40% of E = 25% of R.
i.e. 0.4E = 0.25R -> E / R = 5 / 8
Apparently, it seems that R is bigger, but if you consider E and R to be negative the opposite would be true.
Hence, option (A) is correct.
i.e. 0.4E = 0.25R -> E / R = 5 / 8
Apparently, it seems that R is bigger, but if you consider E and R to be negative the opposite would be true.
Hence, option (A) is correct.
Most Upvoted Answer
When 40% of a number E is added to another number R, B becomes 125% of...
Let's start by translating the given information into equations:
- "40% of a number E": this can be written as 0.4E
- "added to another number R": we add 0.4E to R, so we get R + 0.4E
- "B becomes 125% of its previous value": if we call the previous value of B "B0", then we have B = 1.25B0
Putting it all together, we can write:
R + 0.4E = 1.25B0
But we don't know anything about B0, so we need to find another equation to solve for E and R. We can use the fact that B is a certain percentage of its previous value:
B = 1.25B0 = 1.25(B/1.25) = B/0.8
This means that B is 0.8 times its current value. So we can write:
B = 0.8(R + 0.4E)
Now we have two equations with two unknowns, E and R:
R + 0.4E = 1.25B0
B = 0.8(R + 0.4E)
We can solve for E by substituting the second equation into the first:
R + 0.4E = 1.25(0.8(R + 0.4E))
Simplifying:
R + 0.4E = R + 1.0E
0.6E = R
So we have found that 0.6E = R. We can substitute this into either equation to solve for E or R. For example, using the second equation:
B = 0.8(R + 0.4E)
B = 0.8(0.6E + 0.4E)
B = 0.8E
So we have found that B is 0.8 times E. This means that either (a) or (b) can be true depending on the values of E and R:
(a) If E = 1 and R = 0.6, then R + 0.4E = 1 and B = 0.8E = 0.8, which satisfies the conditions.
(b) If E = 0 and R = 0, then R + 0.4E = 0 and B = 0, which also satisfies the conditions.
- "40% of a number E": this can be written as 0.4E
- "added to another number R": we add 0.4E to R, so we get R + 0.4E
- "B becomes 125% of its previous value": if we call the previous value of B "B0", then we have B = 1.25B0
Putting it all together, we can write:
R + 0.4E = 1.25B0
But we don't know anything about B0, so we need to find another equation to solve for E and R. We can use the fact that B is a certain percentage of its previous value:
B = 1.25B0 = 1.25(B/1.25) = B/0.8
This means that B is 0.8 times its current value. So we can write:
B = 0.8(R + 0.4E)
Now we have two equations with two unknowns, E and R:
R + 0.4E = 1.25B0
B = 0.8(R + 0.4E)
We can solve for E by substituting the second equation into the first:
R + 0.4E = 1.25(0.8(R + 0.4E))
Simplifying:
R + 0.4E = R + 1.0E
0.6E = R
So we have found that 0.6E = R. We can substitute this into either equation to solve for E or R. For example, using the second equation:
B = 0.8(R + 0.4E)
B = 0.8(0.6E + 0.4E)
B = 0.8E
So we have found that B is 0.8 times E. This means that either (a) or (b) can be true depending on the values of E and R:
(a) If E = 1 and R = 0.6, then R + 0.4E = 1 and B = 0.8E = 0.8, which satisfies the conditions.
(b) If E = 0 and R = 0, then R + 0.4E = 0 and B = 0, which also satisfies the conditions.
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