A number is divided into two parts in such a way that 50% of 1st part is 4 more than 40 % of 2nd part and 70% of 1st part is 2 more than 60% of the 2nd part, then the number is?

170

ATQ,

⇒ 50% A - 40% B = 4     ..........(i)

⇒ 70% A - 60% B = 2   ..........(ii)

(i) × 3 and (ii) × 2 and subtract, we get

⇒ 150% A - 120% B   = 12

⇒ -140% A + 120% B = -4 

⇒                   10% A = 8

⇒                           A = 80

Value of A putting in equation (i)

⇒ 50% × 80 - 40% B = 4

⇒ \(\frac{1}{2}\) × 80 - \(\frac{2}{5}\) B = 4

⇒ 40 - \(\frac{2}{5}\)B = 4

⇒ \(\frac{2}{5}\)B = 36

⇒ B = 36 × \(\frac{5}{2}\)

⇒ B = 90

⇒ Hence the number is (A + B) = 80 + 90 = 170