Question

A sum of Rs. 4,360 was to be divided among A, B, C and D in the ratio of 3 : 4 : 5 : 8, but it was divided in the ratio of 1 1 1 1
: : :
3 4 5 8
by mistake. As a result:

Answer 1

A sum of Rs. 4,360 in the ratio of 1/3: ¼ : 1/5 : 1/8 among A, B, C and D instead of 3 : 4 : 5 : 8 by mistake, as a result of this A get Rs. 946 more.

Step-by-step explanation:

The original ratio into which a sum of Rs. 4360 was to be divided = 3:4:5:8 ….. (i)

The incorrect ratio into which the sum was divided by mistake

= $\frac{1}{3} : \frac{1}{4} : \frac{1}{5} : \frac{1}{8}$

multiplying each of ratio with the L.C.M of the denominator = 120

= $120* \frac{1}{3} : 120 * \frac{1}{4} : 120 * \frac{1}{5} : 120 * \frac{1}{8}$

= 40 : 30 : 24 : 15 ….. (ii)

Therefore, from (i) & (ii) we can clearly see that A gets more money due to the mistake.

Now,

A’s share of money in the original ratio = [3/{3+4+5+8}]*4360 = [3/20]*4360 = Rs. 654

And,

A’s share of money in the incorrect ratio = [40/{40+30+24+15}]*4360 = [40/109]*4360 = Rs. 1600

∴ Difference in the A’s share of money = 1600 – 654 = Rs. 946

Thus, as a result of the mistake, A gets Rs. 946 more.

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