If P:Q = 1/2:1/3 and Q:R = 3/2 : 4/3 , find P:R
Answers
Answer:9/4
Step-by-step explanation:
P:Q=1/2:1/3=3:2
Q:R=3:2
P:R=P:Q*Q:R
=3:2*3:2=9/4
Step-by-step explanation:
Given :-
P:Q = 1/2:1/3
Q:R = 3/2 : 4/3
To find:-
Find P:R ?
Solution:-
Given that :
P:Q = 1/2:1/3
=> P/Q = (1/2)/(1/3)
=> P/Q = (1/2)×(3/1)
=> P/Q = (1×3)/(2×1)
=> P/Q = 3/2
=> P:Q = 3:2------------(1)
and
Q:R = 3/2 : 4/3
=> Q/R = (3/2)/(4/3)
=> Q/R = (3/2)×(3/4)
=>Q/R = (3×3)/(2×4)
=> Q/R = 9/8
=> Q:R = 9:8 -----------(2)
For equating Q terms
On taking (1)
P/Q = 3/2
=> P/Q = (3/2)×(9/9)
=> P/Q = (3×9)/(2×9)
=> P/Q = 27/18
=> P:Q = 27:18 ---------(3)
On taking (2)
Q/R = 9/8
=> Q/R = (9/8)×(2/2)
=>Q/R = (9×2)/(8×2)
=> Q/R = 18/16
Q:R = 18:16 ----------(4)
Now,
P:Q = 27:18
Q:R = 18:16
_______________
P:Q:R = 27:18:16
_______________
Now, P:R = 27:16
Alternative method:-
Given that :
P:Q = 1/2:1/3
=> P/Q = (1/2)/(1/3)
=> P/Q = (1/2)×(3/1)
=> P/Q = (1×3)/(2×1)
=> P/Q = 3/2
=> P:Q = 3:2------------(1)
and
Q:R = 3/2 : 4/3
=> Q/R = (3/2)/(4/3)
=> Q/R = (3/2)×(3/4)
=>Q/R = (3×3)/(2×4)
=> Q/R = 9/8
=> Q:R = 9:8 -----------(2)
From (1)&(2)
We have , P/Q = 3/2
Q/R = 9/8
P/R = (P/Q)×(Q/R)
=>P/R = (3/2)×(9/8)
=>P/R = (3×9)/(2×8)
=>P/R = 27/16
=> P:R = 27:16
Answer:-
The value of P:R for the given problem is 27:16
Used formulae:-
- a:b can be written as a/b
- a/c = (a/b)×(b/c)