Prime Time Class 6 Long Question Answer

Prime Time Class 6 Long Question Answer

Prime Time Class 6 Long Question Answer

Question 1.

In a colony of 100 blocks of flats numbering 1 to 100, a school van stops at every sixth block, while a school bus stops at every 10th block. If the two vehicles start from the satne entrance of the colony, on which blocks will the school van stop and on which blocks will the school bus stop ? On which blocks lyill of both of these vehicles stop ?

Solution:

School van will stop at 6th, 12th, 18th, ..., 84th, 90th and 96th blocks (multiples of 6).

School bus will stop at 10th, 20th, 30th, ..., 70th, 80th, 90th and 100th blocks (multiples of 10).

So, both of these will stop at the common multiples of 6 and 10 that is 30th, 60th and 90th blocks.

Question 2.

The floor of a room is 896 cm long and 672 cm broad. What is the greatest side (in cm) of the square tiles that can cover the floor exactly ? How many such tiles will be needed for this purpose ?

Solution:

The greatest side (in cm) of the square tiles will be greatest common factor of 896 and 672. Now, factors of 896 = 1, 2, 4, 7, 8, 14, 16, 56, 64, 112, 128, 224, 448 and 896.

Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336 and 672.

Common factors are 1, 2, 4, 7, 8, 14, 16, 56, 112 and 224, ...

Greatest common factor = 224.

So, greatest side of the square tile = 224 cm

Hence, number of tiles required

= [latex]\frac{896 \times 672}{224 \times 224}[/latex] = 4 x 3 = 12.