A family has 4 earning members P, Q, R, S. In 2011 their respective shares in the total income was 25%, 35%, 10%, 30% respectively. They spend 40% of the total income and save the remaining. In 2012 P's salary went up by 20%, Q's salary increased by 20% and R's salary decreased by 10% and S's salary decreased by 20%. In 2012 what percent of total family income should they spend to save same amount as in 2011?
Solution
Let total salary of the family be 100.
In 2011 the family saved = 100 - 40 = 60
Total income in 2012
$= (25 \times 1.2) + (35 \times 1.2) + (10 \times 0.9) + (30 \times 0.8) = 105$
Required$\% = \dfrac{45}{105} \times 100 = 42.8\%$