Question

Three friends went to a hotel and had breakfast to their taste, paying $Rs.16,Rs.17$ and $Rs.21$ respectively
(i) Find their mean expenditure.(ii) If they have spent $3$ times the amount that they have already spent, what would their mean expenditure be?
(iii) If the hotel manager offers $50\%$ discount, what would their mean expenditure be?
(iv) Do you notice any relationship between the change in expenditure and the change in mean expenditure?

Answer 1

Let three friends be A, B and C

According to the question,

Expenditure of A $=Rs.16$

Expenditure of B $=Rs.17$

Expenditure of C $=Rs.21$

(i) Their mean expenditure

$=\frac{16+17+21}{3}=\frac{54}{3}=Rs.18$

(ii) New expenditure of A $=Rs.16\times 3=Rs.48$

New expenditure of B $=Rs.17\times 3=Rs.51$

New expenditure of C $=Rs.21\times 3=Rs.63$

Their new mean expenditure

$=\frac{48+51+63}{3}=\frac{162}{3}=Rs.54$

(iii) Total amount $=Rs.54$

After $50\%$ discount, net amount to be paid $=54\times \frac{50}{100}=Rs.27$

Their mean expenditure is,

$=\frac{27}{3}=Rs.9$

(iv) New expenditure $=3\times$ Original one

And, New mean expenditure $=3\times$ Original one (Mean expenditure)

The change in the expenditure and the change in the mean expenditure are proportionate to each other.