Since 653xy is divisible by 2 as well as by 5, so y = 0 Now 653x0 is divisible by 8 so 3x0 is also divisible by 8. By hit and trial x=6 and x+y = 6

Answer:44 Explanation: HCF of 108,180,240 is 12. Now for oranges required boxes =108/12=9 Similarly for apple=180/12=15 For pears 240/12=20 Total boxes required 9+15+20=44 Hence proved.

Answer:3 Explanation:327/9 gives 3 remainder 422/9 gives 8 remainder and 955/9 gives 1 as a remainder.adding all 3 remainders wer Have 12 whwn divided by 9 it gives 3. Hence proved.

Let the quantity of the wine in the cask originally be x litres.

Using formula: 

Final Amount of solute that is not replaced= Initial Amount ×(Vol. after removal/Vol. after replacing)n

                                                                                       Or

Final ratio of solute not replaced to total = Initial ratio ×(Vol. after removal/Vol. after replacing)n

Then ratio of wine to total solution in cask after 4 operations:

⇒1×(x−8/x)4=16/81

 (considering 2nd formula here)

⇒ (x−8)/x=2/3

 ⇒ 3x−24=2x

⇒ x=24 litres.

Here, CP of unit quantity of Dearer = 460 per kg , 

CP of unit quantity of Cheaper = 410 per kg 

So we can use above formulas : 

Quantity of cheaper/Quantity of dearer =

{C.P of dearer-Mean price}/{Mean price-C.P of cheaper}

460-430/430-410=30/20=3/2