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Standard XII

Mathematics

Sum of n Terms

A says, "If B...

Question

A says, "If B gives me Rs. 40 he will have half as much as C. But if C gives me Rs. 40 then three of us will have the same amount. What is the total amount of money that A, B and C have among them ?

240

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320

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360

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420

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Solution

The correct option is C 360
Let A has $R s$ $a$
B has $R s$ $b$
C has $R s$ $c$
Now, According to question,
$b - 40 = \frac{c}{2}$
$2 b - 80 = c$ (I)
Also, $a + 40 = b = c - 40$ (II)
thus, from I and II,
$2 b - 80 = b + 40$
$b = 120$
Hence, $a = b - 40 = 120 - 40 = 80$
and, $c = 2 b - 80 = 2 \times 120 - 80 = 160$
Total amount = $a + b + c = 80 + 120 + 160 = 360$

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A says, "If B gives me Rs. 40 he will have half as much as C. But if C gives me Rs. 40 then three of us will have the same amount. What is the total amount of money that A, B and C have among them ?

The correct option is C 360Let A has Rs aB has Rs bC has Rs cNow, According to question,b−40=c22b−80=c (I)Also, a+40=b=c−40 (II)thus, from I and II,2b−80=b+40b=120Hence, a=b−40=120−40=80and, c=2b−80=2×120−80=160Total amount = a+b+c=80+120+160=360