Question

Weights of two friends ram and sham are in the ratio 4:5. if ram's weight is increased by 10% and total weight of ram and shyam become 82.8 kg, with an increases of 15%, by what percent did the weight of shyam has to be increased?

Answer 1

Therefore the weight of shyam has to be increased=$\frac{46-40}{40} \times 100 \%$

                                                                                       =15%

Step-by-step explanation:

Given weight of two friends Ram and shyam are in ratio 4:5 .

Let the weight of Ram be 4x and sham be 5x.

Total weight of Ram and shyam is = 4x +5x = 9x

Since Ram's weight is increases by 10% .

Now Ram's weight is = $4x \times \frac{100+10}{100}$

                                  $=4x \times \frac{110}{100}$

Total  weight Ram and Shyam become 82.8 kg with an increases of 15%.

Again total weight of Ram and Shyam=$4x \times \frac{100+15}{100}$

                                                              $=4x\times \frac{115}{100}$

According to the problem,

$9x\times \frac{115}{100}= 82.8$

$\Leftrightarrow x=\frac{82.8 \times 100}{115\times 9}$

$\Leftrightarrow x = 8$

Therefore Shyam's weight= 5x kg= 5× 8 kg =40 kg

New weight of Ram is  $=4x\times \frac{115}{100}$

                                       $=4\times 8 \times\frac{115}{100}$

                                       =36.8 kg

New weight of Shyam = 82.8 - 36.8

                                      =46kg

Therefore the weight of shyam has to be increased=$\frac{46-40}{40} \times 100 \%$

                                                                                       =15%

Answer 2

Answer:

19%

Step-by-step explanation:

Given:

Ram's age be 4x, Shyam's age be 5x.

Total weight is 9x

Ram's age increases by 10%.

New total weight with 15% increase= 82.8 kg

Now, to find x:

New total weight (15% increase from original)

= $9x + 9x*\frac{15}{100}$

$=9x*\frac{115}{100} = 82.8$ (The given value)

Equating for x we get

x=8

Now we calculate Shyam's original weight (required for percentage calculation)

=5*8= 40 years

Shyam's new age:

$=4*8(1+\frac{10}{100} )\\=32*\frac{110}{100}\\=35.2 years$

We know,

Total new age= Ram's new age  + Shyam's new age

Therefore, Shyam's new age = 82.8 - 35.2 years = 47.6 years

Let increased percentage be y.

$=40* (1+\frac{y}{100} )=47.6\\\\=\frac{y}{100} = \frac{47.6}{40} - 1\\= y = 19%$%

Hence the answer is 19%.

Hope it helps. I tried my best to give the most detailed explanation!