Question

2. The least number which divided by 5, 6, 7 and 8
leaves a remainder 3, but when divided by 9
leaves no remainder is
​

Answer 1

If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9. Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder

Answer 2

Let, Breadth of rectangle be x m.

And, Length of rectangle be 3x + 5 m. [We take length be 3x + 5 m because it is given that length is five meter more than thrice the Breadth.]

We know,

Perimeter of rectangle = 2(Length + breadth)

Put the values :

⟶ 74= 2×(3x + 5 + x)

⟶ 74 = 6x + 10 + 2x

⟶ 74 = 8x + 10

⟶ 74 - 10 = 8x

⟶ 64 = 8x

⟶ 64/8 = x

⟶ x = 8

Verification:-

⟶ 74 = 2× (3x + 5 + x)

Put x = 8

⟶ 74 = 2×(3×8 + 5 + 8)

⟶ 74 = 2×(24 + 5 + 8)

⟶ 74 = 2×(29 + 8)

⟶ 74 = 58 + 16

⟶ 74 = 74

Now,

We take,

Breadth be x. So, Breadth of rectangle is 8 m.

Length be 3x + 5 = 3×8 + 5 = 29. Thus, Length of rectangle is 29 m.