Question

Saakar had a number of toys to distribute among children. At first, he gave 2 toys to
child, then 3, then 4, then 5, then 6, but was always left with one. On trying 7 he had none left What is the smallest number of toys that he could have had?
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Answer 1

Given : Saakar had a number of toys to distribute among children

he gave 2 toys to  child, then 3, then 4, then 5, then 6, but was always left with one

On trying 7 he had none left

To Find : smallest number of toys that he could have had

Solution:

Toys  = 2A + 1

3B + 1

4C + 1

5D + 1

6E + 1

7F

=> T - 1 = 2A = 3B = 4C = 5D = 6E

LCM of 2 , 3 , 4 , 5 & 6

= 60

T - 1 = 60K

T = 60K + 1

60K  + 1  = 7F

4K + 56K + 1 = 7F

=> 4K + 1  = 7(F - 8K)

K = 5

=> F - 8K = 3

=> F - 40 = 3

=> F = 43

 

7F = 7 x 43 = 301

301 TOYS

301 = 2x 150 + 1

3 x 100 + 1

4 x 75 + 1

5 x 60 + 1

6 x 50 + 1

7 x 43

smallest number of toys that he could have had = 343

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Answer 2

Answer:

For the answer, please see the photos attached.

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