Question:Find the largest number which divides 62, 132 and 237 to leave the same reminder in each case. 

Required number = H.C.F of (132-62), (237-132) & (237-62)
                       = H.C.F of 70, 105 & 175 = 35.

Question:Find the largest number of four digits  exactly divisible by 12, 15, 18 and 27. 

The largest number of four digits is 9999.
Required number must be divisible by 1 c.m of 12, 15, 18, 27 i.e. by 540.
On dividing 9999 by 540, we get 279 as remainder.
`:.` Required number = (9999-279) = 9720.

Question:Find the smallest number of five digits exactly divisible by 16, 24, 36 and 54. 

The smallest number of five digits is 10000.
Required number must be divisible by 1 c.m of 16, 24, 36, 54 i.e. 432.
On dividing 10000 by 432, we get 64 as remainder.
`:.` Required number = 10000+ (432-64) = 10368.

Question:Evaluate:
(i) 617 + 6.017 +.617 +6.0017 = ? 

617 + 6.017 +.617 +6.0017 =629.6357

Question:5.064 + 3.98 + .7036 + 7.6 + .3 + 2 = ? 

5.064 + 3.98 + .7036 + 7.6 + .3 + 2 =19.6476

Question:31.004 - 17.2386 =? 

31.004 - 17.2386 = 13.7654

Question:13 - 5.1967 = ? 

13 - 5.1967 = 7.8033

Question:(i) 67.32 + ? =431.146

(ii) 107.07 - ? =63.932 

(i) Let 67.32 + x =431.146

 Then x=(431.146 - 67.32)

 :. x = 363.826


 (ii) Let 107 - x =63.932

 Then x = (107 - 63.932)

 :. x = 43.138

Question:Find the products:
 (i) `6,3204 xx 100`

 (ii) `0.5791 xx 1000`

 (iii) `0.069 xx 10000` 

(i) `6,3204 xx 100 = 632.04`

 (ii) `0.5791 xx 1000 = 579.1`

 (iii) `0.069 xx 10000 = 690`

Question:Find the products:
(i) 2.61 x 1.3
(ii) 2.1693 x 1.4
(iii) .4 x .04 x .004 x 40 

(i) 261 x 13 = 3393 
The sum of decimal places of given numbers = (2 + 1) = 3
`:.` 2.61 x 1.3 = 3.393

(ii)  21693 x 14 = 303702
Sum of the decimal places =(4 + 1) =5
`:.` 2.1693 x 1.4 = 3.03702

(iii)  4 x 4 x 4 x 40 = 2560
Sum of the decimal places =(1 + 2 +3) =5
`:.`  .4 x .04 x .004 x 40 =.002560