A number leaves remainder 3 when divided by 8, and the quotient so obtained leaves remainder 2 when divided by 5. The least such number is:

The quotient must be of the form $5k+2$, and the smallest choice is 2 (taking $k=0$). Then the number is $8\times 2+3=19$. Check: 19 ÷ 8 gives quotient 2 and remainder 3, and 2 ÷ 5 gives remainder 2. Using the divisor 5 as the quotient instead gives the wrong value 43.