Discussion

Explanation:

Total number of blocks arranged on:
Day 1 = 31
Day 2 = 65 – 31 = 34
Day 3 = 98 – 65 = 33
Day 4 = 136 – 98 = 38
Day 5 = 169 – 136 = 33

Let number of blocks arranged on a day by Achal, Jitesh, Karthik, Pratyush and Tapish be A, J, K, P and T.

(1) ⇒ J = A - 1
(2) ⇒ J = K + 2
(3) ⇒ P = K + 3
(4) ⇒ P = T + 6
(5) ⇒ A = T – 5

On a day if all 5 persons arrange blocks and if K arranges x blocks,
(2) ⇒ J arranges x + 2 blocks
(1) ⇒ A arranges x + 3 blocks,
(3) ⇒ P arranges x + 3 blocks,
(4) ⇒ T arranges x – 3 blocks,
(5) ⇒ A arranges x – 8 blocks

Now, (2) and (5) are contradictory, hence all 5 cannot arrange blocks on any day.

Now considering cases where exactly 4 persons arrange blocks on a particular day:

On a day if all 4 persons except T arrange blocks ad if K arranges x blocks,
(2) ⇒ J arranges x + 2 blocks
(1) ⇒ A arranges x + 3 blocks,
(3) ⇒ P arranges x + 3 blocks,
Total blocks arranged on this day = 4x + 8

On a day if all 4 persons except P arrange blocks and if K arranges x blocks,
(2) ⇒ J arranges x + 2 blocks
(1) ⇒ A arranges x + 3 blocks,
(5) ⇒ T arranges x + 8 blocks
Total blocks arranged on this day = 4x + 13

On a day if all 4 persons except J arrange blocks if K arranges x blocks,
(3) ⇒ P arranges x + 3 blocks,
(4) ⇒ T arranges x – 3 blocks,
(5) ⇒ A arranges x – 8 blocks
Total blocks arranged on this day = 4x - 8

On a day if all 4 persons except A arrange blocks if K arranges x blocks,
(2) ⇒ J arranges x + 2 blocks
(3) ⇒ P arranges x + 3 blocks,
(4) ⇒ T arranges x – 3 blocks,
Total blocks arranged on this day = 4x + 2

On a day if all 4 persons except K arrange blocks and if J arranges x blocks,
(1) ⇒ A = x + 1
(5) ⇒ T = x + 6
(4) ⇒ P = x + 12
Total blocks arranged on this day = 4x + 19

Now, number of blocks arranged on day 1 = 31.

If T is not working ⇒ 4x + 8 = 31.
This is rejected as x should be an integer.

If P is not working ⇒ 4x + 13 = 31.
This is rejected as x should be an integer.

If J is not working ⇒ 4x - 8 = 31.
This is rejected as x should be an integer.

If A is not working ⇒ 4x + 2 = 31.
This is rejected as x should be an integer.

If K is not working ⇒ 4x + 19 = 31.
⇒ x = 3
∴ On day 1 number of blocks arranged by each of them is J = 3, A = 4, T = 9 and P = 15

Similarly, we can calculate blocks arranged for remaining 4 days as well.

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Tapish arranges a total of 9 + 5 + 13 + 6 + 13 = 46 blocks,

Hence, 46.

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