27. Four friends P, Q, R and S have some money. The
amount with P equals the total amount with the
others. The amount with Q equals one-third of
the total amount with the others. The amount
with R equals one-fifth of the total amount
with the others. The amount with S equals one-
eleventh of the total amount with the others. The
sum of the smallest and the largest amounts with
them is 1210. Find the sum of the amounts with
the other two (in rs).
Answers
Answer:
As given in the question,
P = Q + R + S …… (i)
Q = 1/3 [P + R + S] ….. (ii)
R = 1/5 [P + Q + S] ….. (iii)
S = 1/11 [P + Q + R] ……. (iv)
On subtracting eq. (i) & (ii), we get
P – 3Q = Q + R + S - [P + R + S]
⇒ P – 3Q = Q – P
⇒ 2P = 4Q
⇒ P = 2Q ….. (v)
And,
On subtracting eq. (iii) & (iv), we get
5R – 11S = [P + Q + S] - [P + Q + R]
⇒ 5R – 11S = S - R
⇒ 6R = 12S
⇒ R = 2S ….. (vi)
Substituting the values of (v) & (vi) in (i), we get
2Q = Q + 2S + S
⇒ Q = 3S …… (vii)
∴ P = 2 * 3S = 6S …… [substituting Q = 3S in eq. (v)] …..... (viii)
We are also given that, the sum of the smallest and the largest amounts with P, Q, R & S is Rs. 1210.
From (viii), (vii) & (vi), we get
P=6S < Q=3S < R=2S < S
So, the largest amount is with P and the smallest amount is with S.
Therefore,
P + S = 1210
⇒ 6S + S = 1210 …. [from (vii) & (viii)]
⇒ 7S = 1210
⇒ S = 1210 / 7 = Rs. 172.85
Thus,
The sum of amounts with other two, i.e., Q & R is,
= Q + R
= 3S + 2S ….. [values of Q & R from (vii) & (viii)]
= 5S
= 5 * 172.85 ….. [value of S = 172.85]
= Rs. 864.25
864.25
Step-by-step explanation:
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