Question

The average weight of 8 men is increased by 1.5kg when one of the men who weighs 65 kg is replaced by a new man. The weight of the new man is

Answer 1

Answer:

77 kg is the weight of the new man.

Step-by-step explanation:

$\bold{\underline{\underline{Method\:1)}}}$

Average weight of 8 person is increased by 1.5 kg.

⇒ (8 × 1.5) kg

⇒ 12 kg

Another man weighs 65 kg is replaced by new man.

We have to find the weight of the new man.

To find the weight of the new man. We have to add the weight of the first man and weight of the another man after replacement.

i.e.

⇒ (65 + 12) kg

⇒ 77 kg

∴ 77 kg is the weight of the new man.

$\bold{\underline{\underline{Method \:2)}}}$

Let take -

• weight of one man = 65 kg

Average weight of 8 person is increased by 1.5 kg.

Means, weight of each person is increased by 1.5 kg.

So, sum of weight of one man and product of 5 persons weight.

i.e.

⇒ 65 + (1.5 × 8)

⇒ 65 + 12

⇒ 77 kg

∴ 77 kg is the weight of the new man.

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Weight\:of\:new\:man=77\:kg}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about average weight of 8 men is increased by 1.5kg when one of the men who weighs 65 kg is replaced by a new man.

• We have to find the weight of the new man.

$\underline \bold{Given : } \\ \implies Weight \: of \: one \: man = 65 \: kg \\ \\ \underline \bold{To \: Find : } \\ \implies Weight \: of \: new \: man = ?$

• According to given question :

$\bold{Avg. \: weight \: of \: 8 \: man \: increased \: by \: 1.5 \: kg} \\ \implies 8 \times 1.5 \: kg \\ \\ \implies 12 \: kg \\ \\ \bold{For \: new \: man \: Weight : } \\ \implies new \: man \: Weight = Weight \: of \: man \: replaced + 12 \\ \\ \implies New \: Weight = 65 + 12 \\ \\ \bold{\implies New \: Weight = 77 \: kg}$

$\bold{Second \: method : } \\ \\ \bold{Let \: Avg. \: Weight \: of \: 8 \: men = x \: kg} \\ \\ \implies sum \: of \:their \: Weight = 8x \: kg\\ \\ \implies New \: Avg. \: weight = (x + 1.5) \: kg \\ \\ \bold{For \: New \: man \: weight : } \\ \implies New \: Avg. \: Weight = \frac{Sum \: of \: their \: weight - Weight \: of \: man+ Weight \: of \: new \: man}{Number \: of \: men} \\ \\ \implies x + 1.5 = \frac{8x - 65 + new \: weight}{8} \\ \\ \implies 8x + 12 = 8x - 65 + new \: weight \\ \\ \implies \cancel{8x }- \cancel{ 8x} + 12 + 65 =new \: weight \\ \\ \bold{\implies New \: Weight = 77 \: kg}\\ \\\bold{ \therefore Weight \: of \: new \: man \: is \: 77 \: kg}$