Question

The incomes of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio 8 : 5 : 2. If C spends 2000 rupees and B saves 700 rupees, then A saves <br />a) 1500 rupees<br />b) 1000 rupees<br />c) 500 rupees<br />d) 250 rupees​

Answer 1

Answer:

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Let the expenses of A, B and C be rupees 8x, rupees 5x and rupees 2x respectively. Given, 2x = 2000

=> x = 1000 rupees

=> B's expenses = 5 × 1000 = 5000 rupees

A's expenses = 8000 rupees

Given, B's savings = 700 rupees

=> B's income = 5000 rupees + 700 rupees = 5700 rupees.

Given, A's income : B's income = 5 : 3

=> A's income/5700 = 5/3

=> A's income = 5/3

=> A's income = 5/3 × 5700 = 9500 rupees.

A's savings = 9500 – 8000 = 1500.

Therefore A's savings is 1500 rupees.

Answer 2

Answer:

1500

Step-by-step explanation:

Let A, B & C be the incomes of A, B & C respectively & a, b & c be their expenses respectively.

Given,

A:B = 5:3

i.e. A/B = 5/3

i.e. A = 5B/3 — (i)

Given also,

a:b:c = 8:5:2

i.e. a/b = 8/5 and b/c = 5/2

i.e. a = 8b/5 — (ii) and b = 5c/2 — (iii)

Given also,

c = 2000 — (iv)

Substituting equation (iv) in (iii), we get,

b = 5 * 2000 / 2

i.e. b = 5000 — (v)

Substituting equation (v) in (ii), we get,

a = 8 * 5000 / 5

i.e. a = 8000 — (iv)

Given also,

B - b = 700 — (vii)

Substituting equation (v) in (vii), we get,

B - 5000 = 700

i.e. B = 5700 — (viii)

Substituting equation (viii) in (i), we get,

A = 5 * 5700 / 3

i.e. A = 5 * 1900

i.e. A = 9500 — (ix)

A’s savings can be written as,

A - a

= 9500 - 8000

= 1500

Hence, A’s savings is Rs. 1,500/-.

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