Question

Four friends A,B,C and D together have Rs. 47; with them A & B together have Rs. 27; C & A have Rs. 25; D & A have Rs. 23. How much money does B have?

Answer 1

Hello,

Answer:B have 13 Rupees

Solution:

let the A,B,C and D have a,b,c and d rupees respectively

ATQ

$a + b + c + d = 47.......eq1 \\ \\ a + b = 27 .........eq2\\ \\ a + c = 25..........eq3 \\ \\ a + d = 23........eq4$

put the value of a+d from eq4 into eq1

$b + c + 23 = 47 \\ \\ b + c = 24$
subtract eq3 from above equation

$- a + b = - 1 \: .....eq5$
now add eq5 and eq2

$- a + b + a + b = - 1 + 27 \\ \\ 2b = 26 \\ \\ b = 13$
So , B have 13 rupees in all.


Hope it helps you

Answer 2

A + B + C + D = 47 ------------ [ 1 ]

A + B = 27 ----------------------- [ 2 ]

A + C = 25 ----------------------- [ 3 ]

A + D = 23  ---------------------- [ 4 ]

[ 2 ] + [ 3 ] + [ 4 ] :

3A + B + C + D = 27 + 25 + 23

3A + B + C + D = 75 ---------------------- [ 5 ]

[ 5 ] - [ 1 ] :

2A = 75 - 47

2A = 28

A = 14

Substitute A = 14 into equation [ 2 ] to find B:

A + B = 27

14 + B = 27

B = 27 - 14

B = 13

Answer: B = 13