1378-(A+B+C+D+E)=F. Find A, B, C, D where A=13% of F, B=1% of F, C=6% of 1378-C, D=10% of F+E, and E=280?

E= 280,

C= 6% of 1378 - C => C = (1378 -C) * 6/100

  => 106 C = 1378 * 6 = >  C = 78.

B = F /100 => 100 B = F  -----(1)

A = 13 * F /100 or 100 A = 13 F ---(2)

D = ( F + 280) / 10 => 10D = F + 280 ---(3)

equation 1378 - (A + B + C + D + E ) = F

=> 1378 - (13 F/100 + F/100 + 78 + F/10 + 28  +280) = F

=> 1378 - 78 - 28 - 280 = F + 13F/100 + F/100 + 10F/100

=> 992 * 100 = 100 F + 13 F + F + 10 F

=> 99200 = 124 F => F = 99200/124 = 800.

B = F/100 = 800/100 = 8;

100 A = 13 F = 13 * 800 = 10400 => A = 104,

10 D = F + 280 => 1080 => D = 1080/10 = 108;

so A = 104, B =8, C =78, D =108 , E 280.

verification:

1378 - (104 + 8 + 78 + 108 + 280) = 800

=> 1378 - 578 = 800

=> 800 = 800. verified. Thanks dear for the invitation.

=%(before C) +6%(C) =%

Step i. (*6)/ = C =

E = and part of D is% of E which is .

Deduct above three bold figures from

Step ii. - =

This figure () consists of%(F) +%(A) +1%(B) +%(part of D), OR

=%

Step iii. Calculate A, B, C, D as follows:

A = (*)/ =

B = (*1)/ =8

C = as above

D = {(*)/}+ =

(Alternatively, calculate F = (*)/ = and use this to calculate A, B, C, D as percentages.)