Question

A sum of Rs.\[9000\] is to be distributed among A, B and C in the ratio of \[4:5:6\]. What will be the difference between A’s and C’s shares?
A.Rs\[.{\text{ }}600\]
B.Rs. \[1000\]
C.Rs. \[900\]
D.Rs. \[1200\]

Answer 1

Hint: We can assume amounts of A, B, and C as \[4k\], \[5k,\] and \[6k\] respectively. Now, try to think the sum \[4k{\text{ }} + {\text{ }}5k{\text{ }} + {\text{ }}6k\]should be equal to what?


Complete step by step solution:
Let, the amount of A be \[4k.\]
So, the amount of B will be \[5k\]and the amount of C will be \[6k.\]
Now, according to question a sum of Rs. 9000 is to be distributed among A, B, and C.
Hence, \[4k{\text{ }} + {\text{ }}5k{\text{ }} + {\text{ }}6k{\text{ }} = {\text{ }}9000\]
\[15k{\text{ }} = {\text{ }}9000\]
$k\;\; = \dfrac{{9000}}{{15}} = {\text{ }}600$
A’s share \[{\text{ }} = {\text{ }}4k{\text{ }} = {\text{ }}4600{\text{ }} = {\text{ }}Rs.{\text{ }}2400\]
C’s share \[ = {\text{ }}6k{\text{ }} = {\text{ }}6600{\text{ }} = {\text{ }}Rs.{\text{ }}3600\]
Therefore, difference between A’s share and C’s share,
 \[{\text{ }} = {\text{ }}3600{\text{ }}-{\text{ }}2400{\text{ }} = {\text{ }}Rs.{\text{ }}1200\]
So, option (D)is the Correct option.


Note: Whenever the question ratio is given and we have to find the exact value then we assume values in terms of any variable (as in this question we used \[k\]).
Here, we skipped calculating shares because according to the question we were asked to calculate the difference between shares.