A number is divided into two parts in such a way that 80% of 1st part is 3 more than 60% of 2nd part and 80% of 2nd part is 6 more than 90% of the 1st part. Then the number is:

135

ATQ,

⇒ 80% A - 60% B = 3     ..........(i)

⇒ -90% A + 80% B = 6   ..........(ii)

(i) × 9 and (ii) × 8 and add, we get

⇒  720% A - 540% B   = 27

⇒ -720% A + 640 % B = 48 

⇒                    100% B = 75

⇒                              B = 75

Value of B putting in equation (i)

⇒ 80% A - (60% × 75) = 3

⇒ \(\frac{4}{5}\)A - \(\frac{3}{5}\) × 75 = 3

⇒ \(\frac{4}{5}\)A - 45 = 3

⇒ \(\frac{4}{5}\)A = 48

⇒ A  = 48 × \(\frac{5}{4}\)

⇒ A = 60

⇒ Hence the number is (A + B) = 60 + 75 = 135