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Divide Rs 7000 among P, Q, and R so that P receives 50% of what Q receives and Q receives 50% of what R receives. Find the value of P, Q, R respectively.

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Rs 1000, Rs 2000, Rs 4000

Rs 2000, Rs 4000, Rs 1000

Rs 4000, Rs 1000, Rs 2000

Rs 4000, Rs 2000, Rs 1000

answer is A.

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Detailed Solution

Given that, Rs. 7000 is divided among P, Q, and R.
P receives 50% of what Q receives and Q receives 50% of what R receives.
Let amount received by R be Rs ‘x’.
According to the question:
⇒

Q = 12 R

⇒ Q = 12 x

(i)
Also,
⇒

P = 12 Q

Substitute the value of Q,

⇒ P = 12 12 x = 14 x

(ii)
We know that,

P + Q + R = 7000

Substituting values of P, Q, R:
⇒

14 x + 12 x + x = 7000

[Using (i) & (ii)]
Taking L.C.M. on L.H.S.

⇒ x + 2 x + 4 x 4 = 7000 ⇒ 7 x 4 = 7000 ⇒ x = 7000 × 4 7 ⇒ x = 1000 × 4 ⇒ x = R s 4000

⇒ R = R s 4000

Substituting

x = 4000

in (i) & (ii)

⇒ Q = 12 (x) ⇒ Q = 12 (4000) ⇒ Q = R s 2000

Also,

⇒ P = 14 (x) ⇒ P = 14 (4000) ⇒ P = R s 1000

Values of P, Q, R are Rs 1000, Rs 2000, Rs 4000 respectively.
Hence, option 1 is correct.

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