Ratio and Proprtion
Proportion
When two ratios are equal, i.e. A:B = C:D, the four quantities (A,B,C and D) are said to be proportional, and we say, that A and B; and C and D are in same proportion. In this situation, these quantities A, B, C and D are called terms of proportion.
Qu. 02: Two vessels P and Q contain milk and water mixed in the ratio of 5: 3 and 2: 3 respectively. In what ratio should P and Q be mixed so as to to form a new mixture containing half milk and half water?
Sol: Let us mix P and Q in the ratio of p and q so as to have equal ratio of milk and water. Then,
Let us mix P and Q in the ratio of p and q so as to have equal ratio of milk and water. Then,
Qu. 04: A, B and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn Rs.2340, what will be C's share of the earnings?
Ans: Let the total job be of 24 units (LCM of 6, 8 and 12 is 24).
Then, as given, A does 4 units of work in a day, B does 3 and C does 2 units of work in a day.
Hence, the ratio of their performances is 4: 3: 2. Hence, the share of C will be: (2/9) x 2340 = 2 x 260 = 520 Rs.
Qu. 03: If 20 men or 24 women or 40 boys can do a task in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a task four times as big working for 5 hours a day for 12 days?
Sol: Let the required number of men be P.
Given, 20 men = 24 women = 40 boys.
This is: 5 men = 6 women; and 1 man = 2 boys
Given task = 20 x 12 x 8 man-days.
Since this task becomes 4 times which has to be accomplished by P number of men, 6 women and 2 boys working for 5 hours a day for 12 days, we have:
4 x 20 x 12 x 8 = {P + 5 + 1} x 5 x 12
128 = P + 6. This is, P = 122. The required number of men is 122. Ans.