# Solutions

1. 3
The series is

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6^3 – 1 = 215

7^3 – 1 = 342

8^3 – 1 = 511

9^3 – 1 = 728

10^3 – 1 = 999

2. 1
3. 2
4. 4
5. 5
6. 5;

The quantity of pure milk to be added
= {12 * (7 – 4)}/4 = 9 litres

7. 4

h = height of candles

The first candle consumed in 6 hours and the second in 4 hours.”

first candle shortens by h/6 each hour

second candle shortens by h/4 each hour

height of first candle after t hours = h – th/6 = h(1 – t/6)

height of second candle after t hours = h – th/4 = h(1 – t/4)

h(1 – t/6) = 2h(1 – t/4)

(1 – t/6) = 2(1 – t/4)

1 – t/6 = 2 – t/2

t/2 – t/6 = 1

6t – 2t = 12

t = 12/4 = 3 hours

8. 2

Required time = LCM of 21, 18, 24 min = 504 mins = 8.4 hrs

9. 1;

1 × 2 × 3 × 4 = 24 numbers, it mean at every place digits

will occur six times.

Sum of one column = 6 ( 1 + 2 + 3 + 4) = 60

Hence, sum of all the numbers

= 60 × (100 + 101 + 102 + 103)

= 60 × 1111 = 66660

10. 3

A’s, B’s and C’s 1 day work = 1/20 + 1/30 + 1/100

Total 3 day’s work = 28/300

Total 30 day work = 280/300

Remaining work = 20/300 = 1/15

Now A’s 1 day work = 1/20

Then remaining work = (1/60)/(1/30) = 1/2

Now, B’s then B complete the remaining work in 1/2

Total number of days = 31 1/2 days.

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