Question

L’s income is 125 percent of M’s income and L’s expenditure is 120 percent of M’s expenditure. If L’s income is 180 percent of M’s expenditure, then what is the respective ratio of L’s savings and M’s savings?
1. 12 : 5
2. 15 : 11
3. 5 : 9
4. 17 : 23

Answer 1

Correct Answer - Option 2 : 15 : 11

Given:

L's income = 125% of the M's income

Concept:

Income = Expenditure + Saving

Calculation:

Let us assume income, expenditure and savings of L, and M is (I_L, I_M), (E_L, E_M) and (S_L, S_M) respectively

⇒ I_L = (125/100) × I_M     ----(1)

⇒ E_L = (120/100) × E_M     ----(2)

⇒ I_L = (180/100) × E_M     ----(3)

⇒ Savings of L = (Income of L) - (Expenditure of L)

⇒ S_L = I_L - E_L

⇒ S_L = {(180/100) × E_M} - {(120/100) × EM}

⇒ S_L = 1.8E_M - 1.2E_M = 0.6E_M     ----(4)

⇒ Savings of M = I_M - E_M

⇒ S_M = {(100/125) × I_L} - {(100/180) × I_L} = (11/45) × I_L = (11/45) × (9/5) × E_M = (11/25) × E_M     ----(5)

⇒ By equations (4) and (5)

⇒ \({S_{L}\over S_{M}}\ =\ {15\over 11}\)

∴ The required result will be 15 : 11.