Question

29. The distance (in meters) to which a boy can throw a
stone is inversely proportional to its weight (in kg).
He breaks the stone into 3 pieces whose weights
(in kg) are in the ratio 1:3 : 2. He then throws the
stones one by one. The sum of the distances they
cover is 22 meters. To what distance can he throw
the unbroken stone? (in m)​

Answer 1

GiVen:

• Distance of the stone is inversely proportional to its weight.

• Total distance covered by the stones is 22m.

So, if weights of 3 stones are in the ratio is 1:3:2

Then, the ratio of its distance would be (1/1):(1/3):(1/2) or 6:2:3

AnSwer:

★ Let the 3 distances be 2x, 3x and 6x.

$\sf \implies \: \: 2x +3x + 6x= 11x \\ \\ \sf \implies \: \:11x = 22 \\ \\\sf \implies \: { \underline{ \boxed{ \sf{ \purple{\:x=2 \: }}}}} \: \bigstar$

So, as we have got the value of x let us find the distances,

• 2x = 2 × 2 = 4m
• 3x = 3 × 2 = 6m
• 6x = 6 × 2 = 12m

Here, (1/6)th weight of the stone is at distance of 12 m.

So,

★ The unbroken stone will go :

$\sf \implies (\dfrac{1}{6}) \times 12= 2m.$

Therefore, the distance is 2m.

Answer 2

Answer:2m.

Step-by-step explanation:

As mentioned in the question, distance of stone is inversely proportional to its weight.

so if the weights of 3 stones are in the ratio is 1:3:2 then the ratio of distance will be (1/1):(1/3):(1/2) or 6:2:3

the total distance covered by the stones is 22m.

let three distances be 6x,2x and 3x

then 6x + 2x +3x = 11x

so, 11x = 22

or, x=2

so the distances will be 12m, 4m and 6m respectively for the 3 stones being in the ratio by weights of 1:3:2

here (1/6)th weight of the stone goes 12 m.

so the unbroken stone will go (1/6)*12= 2m.