Question

The daily expenditure of a sports coaching camp is Rs 12200 when there are 30 male and 20 female members.
When the number of females and males increase by 25% and 10% respectively, the daily expenditure turns
out to be Rs 14170. What would have been the daily expenditure (in Rs) if the number of females and males
had increased by 10% and 20% respectively?​

Answer 1

Answer:

Rs 14170

Step-by-step explanation:

30 M + 20 F = Rs 12200

33M + 25 F = Rs 14170

22F + 36M = Rs 14170

Answer 2

Given:

The daily expenditure of a sports coaching camp is Rs 12200 when there are 30 male and 20 female members.

When the number of females and males increased by 25% and 10% respectively, the daily expenditure turns  out to be Rs 14170

To find:

What would have been the daily expenditure (in Rs) if the number of females and males  had increased by 10% and 20% respectively?​

Solution:

Finding the daily expenditure of one male and one female:

Let's assume,

"M" → the daily expenditure of the sports coaching camp for one male

"F" → the daily expenditure of the sports coaching camp for one female

So, the expenditure of Rs. 12200 for 30 males and 20 females, we can form an equation as:

$30M + 20F = 12200$ ..... (i)

After the increase in the number of males and females, we have

No. of the females after a 25% increase = $20 + \frac{25}{100}\times 20 = 20 + 5 = 25$

No. of the males after a 10% increase = $30 + \frac{10}{100}\times 30 = 30 + 3 = 33$

So, the expenditure of Rs. 14170 for 33 males and 25 females, we can another equation as:

$33 M + 25F = 14170$ ..... (ii)

On multiplying by 25 throughout eq. (i), we get

750M + 500F = 305000 ..... (iii)

On multiplying by 20 throughout eq. (ii), we get

660M + 500F = 283400 ..... (iv)

On subtracting eq. (iv) from (iii), we get

750M + 500F = 305000

660M + 500F = 283400

-           -              -

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90M = 21600

--------------------------------------

∴ M = $\frac{21600}{90} = \bold{240}$ ← the daily expenditure of the sports coaching camp for one male

On substituting the value of M in eq. (i), we get

(30 × 240) + 20F = 12200

⇒ 7200 + 20F = 12200

⇒ 20F = 5000

⇒ F = 250 → the daily expenditure of the sports coaching camp for one female

Finding the daily expenditure if the no. of females and males increases by 10% and 20% respectively:

No. of the females after a 10% increase = $20 + \frac{10}{100}\times 20 = 20 + 2 = 22$

No. of the males after a 20% increase = $30 + \frac{20}{100}\times 30 = 30 + 6 = 36$

So, the expenditure for 36 males and 22 females will be:

36M + 22F

substituting the value of M & F, we get

= (36 × 240) + (22 × 250)

= 8640 + 5500

= Rs. 14140

Thus, the daily expenditure (in Rs) if the number of females and males

had increased by 10% and 20% respectively would have been → Rs. 14140

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