Question
How many numbers between 150 and 600 are divisible by
both 5 and 7?Solution
ATQ, Numbers which are multiple of both 5 and 7 are multiples of L.C.M of 5 and 7 i.e. 35 First multiple of 35 between 150 and 600 = 175 = ‘a’ Last multiple of 35 between 150 and 600 = 595 = an Common dierence = 35 = d Let, number of terms = n Using, an = a + (n – 1)d Where 595 = a + (n – 1) × d Or, 595 = 175 + (n – 1) × 35 Or, 35n – 35 = 595 – 175 = 420 So, n = (420 + 35) ÷ 35 = 13
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