Dear Reader,
Below are four problems dealing with basic calculations on ratio.
Question 1
If P:Q = 9:11 and Q:R = 13:15 then which of the following is P:Q:R?
a) 117:143:165 b) 117:195:135 c) 154:143:180 d) none of these
Answer : a) 117:143:165
Solution :
Given that, P:Q = 9:11 and Q:R = 13:15.
The common variable of above two ratios is Q.
Make Q value as same in both ratios:
Q:R = 13:15 = 13x(11/13) : 15x(11/13) = 11 : 15x11/13
Now, P:Q = 9:11 and Q:R = 11: 15x11/13
P:Q:R = 9:11:(15x11)/13 = (9x13) : (11x13) : (15x11x13/13) = (9x13) : (11x13) : (15x11)
117:143:165
Question 2
If X:Y = 5:6 and Y:Z = 10:11 then what will be X:Z?
a) 22:39 b) 27:31 c) 25:33 d) none of these
Answer : c) 25:33
Solution :
Given that, X:Y = 5:6 and Y:Z = 10:11
i.e., X/Y = 5/6 and Y/Z = 10/11
We have to find X:Z
X/Z = (X/Y) x (Y/Z) = (5/6) x (10/11) = 50/66 = 25/33
Hence, X:Z = 25:33.
Question 3
If P:Q = 5:12, Q:R = 4:15 and R:S = 6:7 then P:S is:
a) 2:21 b) 4:15 c) 1:23 d) 3:12
Answer : a) 2:21
Solution :
Given that, P/Q = 5/12, Q/R = 4:15 and R/S = 6/7.
We have to find, P:S
P/S = (P/Q) x (Q/R) x (R/S)
P/S = (5/12) x (4/15) x (6/7) = 2/21
Hence, P:S = 2:21
Question 4
If X:Y:Z = 5:6:7 then (X/Y):(Y/Z):(Z/X) is equal to:
a) 195:120:244 b) 175:180:294 c) 275:280:214 d) none of these
Answer : b) 175:180:294
Solution :
Given that, X:Y:Z = 5:6:7
Let X = 5a, Y = 6a and Z = 7a.
X/Y = 5a/6a = 5/6
Y/Z = 6a/7a = 6/7
Z/X = 7a/5a = 7/5
(X/Y):(Y/Z):(Z/X) = (5/6):(6/7):(7/5) = (5x7x5 / 6x7x5) : (6x5x6 / 7x5x6) : (7x6x7 / 5x6x7)
= (5x7x5) : (6x6x5) : (7x6x7)
= 175:180:294
Hence, the required answer is 175:180:294.
Below are four problems dealing with basic calculations on ratio.
Question 1
If P:Q = 9:11 and Q:R = 13:15 then which of the following is P:Q:R?
a) 117:143:165 b) 117:195:135 c) 154:143:180 d) none of these
Answer : a) 117:143:165
Solution :
Given that, P:Q = 9:11 and Q:R = 13:15.
The common variable of above two ratios is Q.
Make Q value as same in both ratios:
Q:R = 13:15 = 13x(11/13) : 15x(11/13) = 11 : 15x11/13
Now, P:Q = 9:11 and Q:R = 11: 15x11/13
P:Q:R = 9:11:(15x11)/13 = (9x13) : (11x13) : (15x11x13/13) = (9x13) : (11x13) : (15x11)
117:143:165
Question 2
If X:Y = 5:6 and Y:Z = 10:11 then what will be X:Z?
a) 22:39 b) 27:31 c) 25:33 d) none of these
Answer : c) 25:33
Solution :
Given that, X:Y = 5:6 and Y:Z = 10:11
i.e., X/Y = 5/6 and Y/Z = 10/11
We have to find X:Z
X/Z = (X/Y) x (Y/Z) = (5/6) x (10/11) = 50/66 = 25/33
Hence, X:Z = 25:33.
Question 3
If P:Q = 5:12, Q:R = 4:15 and R:S = 6:7 then P:S is:
a) 2:21 b) 4:15 c) 1:23 d) 3:12
Answer : a) 2:21
Solution :
Given that, P/Q = 5/12, Q/R = 4:15 and R/S = 6/7.
We have to find, P:S
P/S = (P/Q) x (Q/R) x (R/S)
P/S = (5/12) x (4/15) x (6/7) = 2/21
Hence, P:S = 2:21
Question 4
If X:Y:Z = 5:6:7 then (X/Y):(Y/Z):(Z/X) is equal to:
a) 195:120:244 b) 175:180:294 c) 275:280:214 d) none of these
Answer : b) 175:180:294
Solution :
Given that, X:Y:Z = 5:6:7
Let X = 5a, Y = 6a and Z = 7a.
X/Y = 5a/6a = 5/6
Y/Z = 6a/7a = 6/7
Z/X = 7a/5a = 7/5
(X/Y):(Y/Z):(Z/X) = (5/6):(6/7):(7/5) = (5x7x5 / 6x7x5) : (6x5x6 / 7x5x6) : (7x6x7 / 5x6x7)
= (5x7x5) : (6x6x5) : (7x6x7)
= 175:180:294
Hence, the required answer is 175:180:294.
