Dear Reader,
Below are four problems based on Ratio and proportion dealing with simple percentage calculations.
Question 1
The salary of two friends Ramu and Raju are in the ratio 4:5. If the salary of each one increases by Rs.6000, then the new ratio becomes 48:55. What is Raju's present salary?
a) Rs.10500 b) Rs.10500 c) Rs.11500 d) Rs.12500
Answer : b) Rs.10500
Solution :
Ratio their salary is 4:5
Let the original salary of Ramu and Raju be 4k and 5k respectively.
After increasing Rs.6000, the ratio becomes 48:55
That is,
(4k+6000)/(5k+6000) = 48/55
55(4k+6000) = 48(5k+6000)
220k+330000 = 240k+288000
20k= 42000
We have to find the original salary of Raju; that is, 5k.
If 20k = 42000 then 5k = 10500.
Hence the required answer is Rs.10500
Question 2
The number of candidates writing three different entrance exams is in the ratio 4:5:6. There is a proposal to increase these numbers of candidates by 40%, 60% and 85% respectively. What will be the ratio of increased numbers?
a) 14:15:16 b) 12:15:19 c)13:19:21 d) none of these
Answer : d) none of these
Solution :
Given ratio of number of candidates is 4:5:6
Let the number of candidates for 3 exams be 4k, 5k and 6k respectively.
After increasing, number of candidates become (140% of 4k), (160% of 5k) & (185% of 6k)
That is, (140x4k)/100, (160x5k)/100 and (185x6k)/100
= 56k/10, 80k/10 and 111k/10
Now, the required new ratio is: 56k/100 : 80k/10 : 111k/10
= 56 : 80 : 111
Hence the answer is option d.
Question 3
The ratio of salary of two persons X and Y is 5:8. If the salary of X increases by 60% and that of Y decreases by 35% then the new ratio of their salaries become 40:27. What is X's salary?
a) Rs.15000 b) Rs.12000 c) Rs.19500 d) data inadequate.
Answer : d) data inadequate
Solution :
Ratio of salary of X and Y is 5:8
Let the original salary of X and Y be Rs.5k and Rs.8k respectively.
After increasing 60%, new salary of X = 160% of 5k = 160x5k/100 = 80k/10 ...(1)
After decreasing 35%, new salary of Y = (100-35)% of 8k = 65% of 8k = 52k/10 ...(2)
Given that, new ratio is 40:27
That is, 80k/10 : 52k/10 = 40/27
This does not give the value of k; so that we cannot find X's exact salary.
Hence the answer is data inadequate.
