Question

Rs.2010 are to be divided among A, B, C in such a way that if A gets Rs.5, then B must get Rs.12 and if B gets Rs.4, then C must get Rs.5.50. The share of C will exceed that of B by ?​

Answer 1

$\large\underline{\sf{Solution-}}$

Total money to be divided = Rs 2010

Given that,

If A gets Rs. 5 then B must get Rs 12.

It means, .

$\rm :\longmapsto\:A:B \: = \: 5 : 12$

Also, Given that

If B gets Rs. 4 then C must get Rs 5.50

It means,

$\rm :\longmapsto\:B:C = 4 : 5.5 = 40 :55 = 8 : 11$

Now,

We have

$\rm :\longmapsto\:A:B \: = \: 5 : 12$

can be rewritten as

$\rm :\longmapsto\:A:B \: = \: 10 : 24 - - - (1)$

and

$\rm :\longmapsto\:B:C = 8 : 11$

can be rewritten as

$\rm :\longmapsto\:B:C = 24 : 33 - - - (2)$

Thus,

From equation (1) and (2), we concluded that

$\rm :\longmapsto\:A:B:C = 10 : 24 : 33$

Let Assume that

• Share of A = 10x

• Share of B = 24x

• Share of C = 33x

According to statement,

Total amount to be divided = Rs 2010

So,

$\rm :\longmapsto\:10x + 24x + 33x = 2010$

$\rm :\longmapsto\:67x = 2010$

$\bf\implies \:x = 30$

Hence,

• Share of A = 10x = 10 × 30 = Rs 300

• Share of B = 24x = 24 × 30 = Rs 720

• Share of C = 33x = 33 × 30 = Rs 990

Thus,

Share of C - Share of B = 990 - 720 = Rs 270

Hence, Share of C exceeds the share of B by Rs 270.