Question

A car was brought in for servicing when its odometer read 2500 km. During the servicing, it was found that the odometer had a fault because of which it always skipped the digits 4 and 6. How much distance had the car actually travelled?

Answer 1

Answer:

Car has traveled 1280kms

Step-by-step explanation:

Starting from the range 0-10,

it skipped 2kms

similarly in the ranges 10-20 and 20-30, it skipped 2kms each

thus till 30kms, it skipped total of 6kms

from 30-39, or again skipped 2kms and then it directly started from 50

thus from 30 to 50, it skipped total of 2+10=12kms-------(40 is inclusive but 50 is exclusive ... so it makes a total of 10km)

From 50 to 59, it again skipped 2kms and then from it directly started from 70.

Similar to previous calculation,

From 50-70 km, it skipped 12km

Thus from 30 to 70, it skipped 24kms

Further, from 70 to 100kms, it will again skip 6km-----(2km, per 10 km range)

Thus till 100km, it skipped a total of 36kms

Similarly, from 0-100, 100-200, 200-300, 300-399kms, it will skip 36kms each.

thus till 399kms, it has skipped total of 36*4=144kms------1

then it will directly start from 500kms thus skipping a total of 100kms

again from 500-599kms, it will skip 36kms and directly start from 700.

Thus from 400 to 700, it skipped 236kms.

From 700 to 1000, it will skip 36*3=108kms

SO PER 1000KMS, CAR SKIPS 488Kms.

From 0-1000 it skips 488kms

from 1000-2000 it again skips 488kms

from 2000-2399 it skips 144kms---(refer 1)

from 2400-2500 it skips 100kms

thus from 0-2500 it skips 488+488+144+100

=1220kms

Thus it has run 2500-1220kms=1280kms

Answer 2

Answer:

1280 km

Step-by-step explanation:

Some one has already answered this question here but still I'll leave the method I use to solve such questions. We can solve this using base systems.

The odometer when it was brought into servicing shows 2500 km now if we think carefully this 2500 is shown because the actual km travel by the car was 2400 but since digits 4 and 6 are skipped, the odometer couldn't display the r in 2400 and displayed 2500.

We now know the odometer wanted to display 2400. This 2400 though was in base 8 as the numbers (4,6) were skipped each time. To know the actual distance the car covered, we need to convert the 2400 in base 8 to ( x ) in base 10. X will be our answer of exact distance traveled.

Converting 2400 in base 8 to base 10 = 8³ x 2 + 8² x 4 + 0 x 8 + 0 x 1

= 512 x 2 + 64 x 4 + 0 + 0

= 1024+256+0+0

= 1280 km