A sum of ₹50 is divided among A, B, and C in such a way that A gets ₹5 less than B, and B gets ₹10 less than C. What is the ratio of their money share?

The correct answer is 2:3:5.

We are told that a total of ₹50 is divided among A, B, and C with two conditions:

  • A gets ₹5 less than B
  • B gets ₹10 less than C

Let us express all amounts in terms of B, since both A and C are defined relative to B.

From the first condition: A gets ₹5 less than B

$A=B-5$

From the second condition: B gets ₹10 less than C, which means C is ₹10 more than B

$C=B+10$

Now, use the total condition: A + B + C = 50

$(B-5)+B+(B+10)=50$

$3B+5=50$

$3B=45$

$B=15$

Now we can find each person's share:

$A=B-5=15-5=\mathrm{₹10}$
$B=\mathrm{₹15}$
$C=B+10=15+10=\mathrm{₹25}$

Verification: A + B + C = 10 + 15 + 25 = ₹50 ✓

Now find the ratio A : B : C:

$A:B:C=10:15:25$

Divide each term by the HCF of 10, 15, and 25, which is 5:

$=\frac{10}{5}:\frac{15}{5}:\frac{25}{5}=2:3:5$

Therefore, the ratio of A's, B's, and C's shares is 2 : 3 : 5.