Question

₹600 को A, B और C में विभाजित किया
जाता है। A के हिस्से के 2/5
भाग से ₹40
अधिक, B के हिस्से के 2/7 भाग से
₹20 अधिक, C के हिस्से के 9/17 भाग से ₹10
अधिक रुपए सभी बराबर-बराबर हैं। A का
हिस्सा कितना है ?
(1) ₹150 (2) ₹170
(3) ₹280 (4) ₹140​

Answer 1

Given:

Rs. 600 is divided among A, B & C.

$\frac{2}{5}$ of A'share + 40 = $\frac{2}{7}$ od B's share + 20 = $\frac{9}{17}$ of C's share + 10

To find:

A's share

Solution:

Let's assume,

"A" → represents the share of A

"B" → represents the share of B

"C" → represents the share of C

Therefore, we can rewrite as,

$\frac{2}{5}A + 40 = \frac{2}{7} B + 20 = \frac{9}{17} C + 10$

So, let's compare as follows:

(i). $\frac{2}{5}A + 40 = \frac{2}{7} B + 20$

$\implies \frac{2}{5}A + 20 = \frac{2}{7} B$

dividing both sides by 2

$\implies \frac{1}{5}A + 10 = \frac{1}{7} B$

$\implies 7[\frac{1}{5}A + 10] = B$

$\implies B = \frac{7}{5}A + 70$ ........ (Equation 1)

(ii). $\frac{2}{5}A + 40 = \frac{9}{17} C + 10$

$\implies \frac{2}{5}A + 30 = \frac{9}{17}C$

dividing both sides by 9

$\implies \frac{2}{45}A + \frac{10}{3} = \frac{1}{17} C$

multiplying both sides by 17

$\implies C = \frac{34}{45}A + \frac{170}{3}$ ........ (Equation 2)

Now, we are also given that 600 is divided among A, B & C,

∴ $A + B + C = 600$

substituting the values of B & C from equation (1) & (2)

$\implies A + \frac{7}{5}A + 70 + \frac{34}{45}A + \frac{170}{3} = 600$

taking lcm of the denominators

$\implies \frac{45A \:+\:63A \:+\: 3150\:+\:34A\:+\:2550}{45} = 600$

$\implies 142A\:+\:5700 = 27000$

$\implies 142A = 27000\:-\:5700$

$\implies 142A = 21300$

$\implies A = \frac{21300}{142}$

$\implies \bold{A = 150}$ ← option (1)

Thus, A's share is ₹ 150.

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