Question

ravi bought 150 apples and 100 oranges for his neighbors.
When he distributed the apples , 17 were left out .
When he distributed the oranges , 5 were left out .

How many neighbors are there ?

answer with steps !!

Answer 1

take Hcf of 150-17 and 100-5
u get Hcf of 133&95 as 19
that's the only possible ans
☺
100% sure

Answer 2

Let number of neighbors = P

A /C to question ,
when he distributed apples , 17 were left out .
use Euclid division Lemma, Let quiotent is Q1 and Q2 in both cases respectively

150 = P.Q1 + 17
(150 - 17) = P.Q1 -----(1)
again,
when, he distributed oranges, 5 were left out

100 = P.Q2 + 5
(100- 5) = P.Q2 -------(2)

now,
you can see that , p is divisible by (150-17) and (100-5) both . the is possible only when ,
P = HCF{ 133, 95}

HCF { 133, 95 } = 19
P = 19

hence, number of neighbors = 19