Two sums of money are divided between A, B, C and D. The first sum is divided between them in the ratio 4 : 6 : 3 : 2 and the second sum is divided in the ratio 3 : 4 : 7 : 6. The second sum is two times the first sum. Who will get the second largest overall share?

Correct option is A

Given:

First sum is divided among A, B, C, D in the ratio: 4 : 6 : 3 : 2

Second sum is divided in the ratio: 3 : 4 : 7 : 6

Second sum = 2 × (First sum)

Solution:

Let the first sum be x.
Then the second sum = 2x

First sum ratio (total parts = 4 + 6 + 3 + 2 = 15):

$$A = \frac{4}{15}x,\quad B = \frac{6}{15}x,\quad C = \frac{3}{15}x,\quad D = \frac{2}{15}x \\[10pt]\text{Second sum ratio: } 3:4:7:6 \Rightarrow \text{Total parts} = 20 \\\ \\A = \frac{3}{20} \cdot 2x = \frac{3}{10}x,\quad B = \frac{4}{20} \cdot 2x = \frac{2}{5}x \\\ \\C = \frac{7}{20} \cdot 2x = \frac{7}{10}x,\quad D = \frac{6}{20} \cdot 2x = \frac{3}{5}x \\[10pt]\text{Total share:} \\A = \frac{4}{15}x + \frac{3}{10}x = \frac{8}{30}x + \frac{9}{30}x = \frac{17}{30}x \\\ \\B = \frac{6}{15}x + \frac{2}{5}x = \frac{12}{30}x + \frac{12}{30}x = \frac{24}{30}x \\\ \\C = \frac{3}{15}x + \frac{7}{10}x = \frac{6}{30}x + \frac{21}{30}x = \frac{27}{30}x \\\ \\D = \frac{2}{15}x + \frac{3}{5}x = \frac{4}{30}x + \frac{18}{30}x = \frac{22}{30}x$$

​Answer: (a) B
B receives the second largest overall share.