An amount of money is to be distributed among P, Q and R in the ratio of 6 : 19 :
7 respectively. If R gives Rs. 200 of his share t0 Q, the ratio among P, Q and R
becomes 3 : 10 : 3 respectively. What was the total amount ?
Answers
Application of Ratios
Answer: Total Amount = Rs 6400
Explanation:
Given that amount of money is to be distributed among P , Q and R in ratio 6 : 19 : 7 respectively .
Also given if R gives Rs 200 to Q , ration among P , Q and R becomes 3 : 10 : 3 respectively.
As initial ratio of amount of money for P , Q and R is 6 : 9 : 7 , lets assume
initial share of P = 6x , initial share of Q = 9x and initial share of R = 7x
So total amount of money = initial share of P + initial share of Q + initial share of R
⇒ total amount of money = 6x + 19x + 7x
⇒ Total amount of money = 32x -----------eq(1)
Now lets use other information that is "if R gives Rs 200 of its share to Q" ,
New share of R = initial share of R - 200 = 7x - 200
And New share of Q = initial share of Q + 200 = 19x + 200
New ratio of P , Q and R is 3 : 10 : 3 ,
lets concentrate on ratio of Q and R
New ratio of Q and R is 10 : 3
⇒ New share of Q : New share of R = 10 : 3
⇒ 19x + 200 : 7x - 200 = 10:3
⇒
⇒3( 19x + 200 ) = 10 ( 7x - 200)
⇒57x + 600 = 70x - 2000
⇒57x - 70x = -2000 - 600
⇒ -13x = -2600
⇒ x = -2600 ÷ -13
⇒ x = 200
On substituting value of x = 200 in equation (1) that is Total amount of money = 32x , we get
Total Amount of Money = 32x = 32 × 200 = Rs 6400
Verification of solution.
Initial share of P = 6x = 6 × 200 = 1200
Initial share of Q = 19x = 19 × 200 = 3800
Initial share of R = 7x = 7 × 200 = 1400
when R gives Rs 200 to Q
New share of P = 1200 [ No change in share of P ]
New share of Q = 3800 + 200 = 4000
New share of R = 1400 - 200 = 1200
Ratio of New share of P , Q , R = 1200 : 4000 : 1200
= (3 × 400) : (10 × 400) : (3 × 400)
= 3 : 10 : 3 which matches with given information.
Hence Total Amount = Rs 6400
Step-by-step explanation:
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