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Ratio and Proportion

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Question : 76 of 112

Marks: +1, -0

A, B and C have to distribute Rs. 1,000 between them, A and C together have Rs. 400 and B and C Rs. 700. How much does C have?

Rs. 100
Rs. 200
Rs. 150
None

Solution:

Concept:

Set up equations from the given totals and solve for

C

using elimination.

Explanation:

Let the amounts with A, B, and C be

A

,

B

,

C

(in Rs.).

From the problem:

A + C = 400

B + C = 700

A + B + C = 1000

Add the first two equations:

(A + C) + (B + C) = 400 + 700

\Rightarrow A + B + 2C = 1100

Now subtract the total equation (

A + B + C = 1000

) from this result:

(A + B + 2C) - (A + B + C) = 1100 - 1000

\Rightarrow C = 100

Thus, C has Rs. 100.

Answer:

Rs. 100

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