Question

Divide Rs. 7,154 among A, B, C and D so that the

shares of A and B are in the ratio 2 : 5, that of

B and C in the ratio 4 : 7 and that of C and D in

the ratio 9 : 13​

Answer 1

Answer:

A= Rs. 504

B= Rs. 1260

C= Rs. 2205

D= Rs. 3185

Step-by-step explanation:

We know that ratio of A and B is 2:5 and that of B and C is 4:7.

In this case, the LCM of the two values of B (ie 5 and 4) is 20.

Therefore we scale up the values of A and C using this value.

$B=20\\A=\frac{20}{5}*2=8\\ C=\frac{20}{4}*7=35$

Now we have the ratio of A:B:C as 8:20:35

We have the ratio of B:C as 20:35 and that of C:D as 9:13

Now, the LCM of the two values of C, ie 35 and 9, is 315.

We scale up the other ratios using this value as;

$C=315\\D=\frac{315}{9}*13=455\\ B=\frac{315}{35}*20=180\\ A=\frac{180}{20}*8=72$

Therefore the ratio of A:B:C:D is 72:180:315:455

Now, from Rs 7154;

A gets

$\frac{72}{(72+180+315+455)}*7154= 504$

B gets

$\frac{180}{(72+180+315+455)}*7154= 1260$

C gets

$\frac{315}{(72+180+315+455)}*7154= 2205$

D gets

$\frac{455}{(72+180+315+455)}*7154= 3185$