Question: Nawab has two sons Saif and Amir who have export businesses. Nawab’s satisfaction/ utility level is given by adding twice of the satisfaction level of Saif with the satisfaction level of Amir. If Saif makes a profit of ₹100, his satisfaction level goes up by 10% and if he suffers a loss of ₹100, his satisfaction level goes down by 10%. If Amir makes a profit of ₹100, his satisfaction level goes up by 5% and if he suffers a loss of ₹100, his satisfaction level goes down by 15%. Currently, Nawab’s satisfaction level is 24 and the satisfaction level of Saif is same as the satisfaction level of Amir. If Saif makes a profit of ₹100 and Amir suffers a loss of ₹100, what is the approximate percentage change in Nawab’s satisfaction level?
∴ Present satisfaction level of both Saif and Amir = 8.
∵ Saif makes a profit of 100, his satisfaction level goes up by 10% ⇒ Saif’s new satisfaction level= 8 × 1.1 = 8.8
∵ Amir suffers a loss of 100, his satisfaction level goes down by 15% ⇒ Amir’s new satisfaction level= 8 × 0.85 = 6.8
∴ Percentage change = (24.4 − 24)/24 × 100 = (0.4 × 100)/24 = 1.66 %.
Hence, option (d).