Question

solve this 24/u+54/d=6.....(1)and 36/u+48/d=8.....(2)​

Answer 1

24/u + 54/d=6.........(1)
By taking lcm,

24d+54u/ud= 6
24d + 54u= 6ud
Divide it by 2,
12d+ 27u = 3ud
Again by 3,
4d+9u= ud.......(3)
Now ,
36/u+ 48/d=8.......... (2)
By taking lcm,

36d+48u/ud = 8
36d+48u= 8ud
18d+ 24u= 4ud
9d+ 12u= 2ud........(4)
( 9d+12u= 2ud)×4 [By simultaneous linear eqn.]
( 4d+9u = ud) ×9
Subtracting eqn (3) from (4)
36d+ 48u= 8ud
36d+ 81u = 9ud
(–) (–) (–)
....................................
–33u= –ud
.......................................
–33= –ud/u
–33= –d
[d=33]
substituting the value of d in eqn (1),
24/u+ 54/33= 6
24/u+1.65= 6
24/u= 6–1.65
24/u= 4.35
24/u = 4.35
24= 4.35u
u= 24/4.35
u=5.5 or 11/2

[Answer. u= 5.5 or 11/2, d= 33]

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