Question

B's income is 20% more than A's and C's income is 20% less than B's income .If the total income of all the three is 1580.find the income of C's.

Answer 1

Answer:

The income of C is Rs. 480.

Step-by-step-explanation:

Let the income of C be x.

From the first condition,

B' income = A's income + 20% of A's income

⇒ B = A + 20% of A

⇒ B = A + ( 20 / 100 ) * A

⇒ B = A + ( 2 / 10 ) * A

⇒ B = A + 0.2 A

⇒ B = 1.2 A

⇒ A = B / 1.2 - - - ( 1 )

From the second condition,

C's income = B's income - 20% of B's income

⇒ x = 1.2 A - 20 % of 1.2 A

⇒ x = 1.2 A - ( 20 / 100 ) * 1.2 A

⇒ x = 1.2 A - ( 2 / 10 ) * 1.2 A

⇒ x = 1.2 A ( 1 - 0.2 )

⇒ x = 1.2 A * 0.8

⇒ x = 0.96 A

⇒ A = x / 0.96 - - - ( 2 )

From equations ( 1 ) & ( 2 ), we get,

B / 1.2 = x / 0.96

⇒ 0.96 B = 1.2 x

⇒ B = ( 1.2 / 0.96 ) x

⇒ B = ( 1.2 * 100 ) / ( 0.96 * 100 ) x

⇒ B = ( 120 / 96 ) x

⇒ B = ( 10 / 8 ) x

⇒ B = ( 5 / 4 ) x

⇒ B = 1.25 x

Now, we have given that,

Total income of all A, B and C is 1580.

∴ A + B + C = 1580

⇒ ( x / 0.96 ) + 1.25 x + x = 1580

⇒ ( x / 0.96 ) + 2.25 x = 1580

⇒ ( x + 2.25 x * 0.96 ) / 0.96 = 1580

⇒ x + 2.25 x * 0.96 = 1580 * 0.96

⇒ 100 ( x + 2.25 x * 0.96 ) = 100 ( 1580 * 0.96 )

⇒ 100x + 2.25 x * 96 = 1580 * 96

⇒ 100x + 216x = 1580 * 96

⇒ 316x = 1580 * 96

⇒ x = ( 1580 * 96 ) / 316

⇒ x = 1580 ÷ 316 * 96

⇒ x = 5 * 96

⇒ x = 480

∴ The income of C is Rs. 480.

Answer 2

Step-by-step explanation:

given :

• B's income = 20%

• C's income = 20%

to find :

• find the income of C's. = ?

• find the income of C's. = ?

solution :

B income :

• income = A + 20% of A

• income = A + (20 / 100) ×A

• income = A+ (2/10) × A

• income = A + 0.2 A

• income =1.2

• income = B/1.2

C's income :

• income = 1.2 A-20 % of 1.2 A

• income= 1.2 A - (20/ 100) × 1.2 A
• income = 1.2 A-(2/10) × 1.2 A
• income = 1.2 A (1-0.2)

• income ⇒ = 1.2 ×0.8
• income = 0.96

• income = x/0.96

• income 1.2 = x/0.96

• income B= → 0.96 B 1.2 x

• income B = (1.2 / 0.96 ) x

• income B = (1.2×100)/(0.96 ×100) x

• income B = ( 120 / 96 ) ×

• incomeB = (10/8) x

• income B = (5/4) x

• income of B= 1.25 x

income of all of = 1580

• income = (x/0.96) +1.25 x + x = 1580

• income = (x/0.96) +2.25 x = 1580

• income = (x+2.25 x ×0.96 ) / 0.96 = 1580

• x + 2.25 x × 0.96

• income = 1580 × 0.96

• income = 100 (x +2.25 x × 0.96 ) = 100 (1580×

• 0.96)

• income = 100x +2.25 x × 96 = 1580×96

• income = 100x + 216x = 1580 ×96

• income = 316x = 1580 × 96

• income = (1580×96) / 316

• income = 1580 - 316 ×96

• income = 5×96

• income = 480

income = 480