Question

A shopkeeper is arranging glasses in his shop. He notices that if he arranges them in groups of 2 or groups of 3 then no glasses are left over. However, if he tries to arrange them in groups of 5 then 3 glasses would be left over. He knows that the number of glasses he has is more than 50 but less than 100. How many glasses does he have?

Answer 1

Answer:

60 glasses he had

Step-by-step explanation:

If He arrange 60 glasses in group 2 then he will divide it in 30 &30.

aur if we arrange sister class in group 3 then we will divide it in 20 ,20 &20.

Thrrefore by arranging it in 2 or 3 group he had no glasses are left.

Answer 2

Answer:

78

Step-by-step explanation:

According to the question

Suppose the shopkeeper has N glasses in his shop.

50<N<100

arranging them in  groups of 2 then no glasses are left over

arranging them in  groups of 3 then no glasses are left over

arranging them in  groups of 5 then 3 glasses are left over

so N is completely divided by 2 or 3 but not by 5 and it has 3 reminder after divided by 5

so LCM of 2 and 3 =6

so N should be a multiplier of 6 and (N-3)should be a multiplier of 5

54,60,66,72,78,84,90,96 will be the multiplier of 6 between 50 and 100

and only 78 will be followed this equation (N-3)/5

so answer will be 78