Ratio and Proportion: Question 4

Worked solution

Part (a): pounds to rupees

The rupees received are directly proportional to the pounds exchanged, so at a fixed rate we simply multiply by the exchange rate.

$\text{rupees} = \text{pounds} \times 355$

Substitute $40$ pounds:

$40 \times 355 = 14200$

$\boxed{\text{Rs } 14{,}200}$

Part (b): rupees to pounds

Now we work in the opposite direction: we know the rupees and want the pounds. Since $\text{rupees} = \text{pounds}\times 355$, we divide by $355$ to undo the multiplication:

$\text{pounds} = \frac{28400}{355}$

$\text{pounds} = 80$

$\boxed{\pounds 80}$

Check: $80 \times 355 = 28{,}400$ ✓

Part (c): ratio as a fraction

The total takings are split rupee cash : foreign-currency notes $= 5 : 2$.

Total number of parts:

$5 + 2 = 7$

Foreign-currency notes correspond to $2$ of these $7$ parts, so the fraction of the total takings that is foreign-currency notes is:

$\boxed{\frac{2}{7}}$

(This is a separate ratio from the exchange rate used in parts (a) and (b). It describes how the day’s total takings are split between rupee cash and foreign-currency notes, not the conversion rate itself.)

Final answers

• (a) Rupees received $=$ Rs 14,200
• (b) Pounds exchanged $=$ £80
• (c) Fraction that is foreign-currency notes $=$ $\dfrac{2}{7}$