Ratio proportion and partnership | Set-2

Question 1: The ratio of the age of a man and his wife is 6:5. After 16 years, the ratio becomes 10:9. Find the husband’s age when the wife was born.
Solution: Let x is husband’s age
And y is the wife’s age.
x/y= 6/5
x=(6/5)y

After 16 years,
(x + 16)/(y + 16) = 10/9
9x + 144 = 10y + 160
9*(6/5)y = `10y + 16
54y – 50y = 80
y=20
Then x = 24
When the wife was born husband’s age = 4 years.

Question 2: There are peacocks and deer in a national park. If the total number of their heads is 200 and that of legs is 500, the number of deer in park is –
Solution: Let x number of peacocks and y number of deer.
Peacock has two legs and deer has four legs.
Given, x + y = 200 …….1
And 2x + 4y= 500 …….2
Solve 1 and 2
we get x = 150 and y = 50
Number of deer in national park is 50.

Question 3: 5 notebook as much as 12 pens, 7 pens as much as 2 geometry, 3 geometry as much as 2 bottles. If the cost of 5 bottles is Rs 875, then find the cost of a notebook.
Solution: 5 bottles = 875
2 bottles = 875 * 2/5 = 3 geometry
2 geometry cost= 875 * 2/5 * 2/3 = 7 pens cost
12 pens cost = 875 * 2/5 * 2/3 * 12/7 = 5 notebook
1 notebook= 875 * 2/5 * 2/3 * 12/7 * 1/5 = Rs 80

Question 4: The difference between two positive numbers is 15 and the ratio between them is 5:2. Find the product of the numbers.
Solution: Let 5x and 2x are the numbers.
5x – 2x = 15
x = 5
Numbers are 25 and 10
Product = 250

Question 5: If x varies inversely as y-1 and is equal to 30 when y=8, find x when y=11.
Solution: x= k/ (y-1)
30 = k/(8-1)
k = 210
Put k=210 and y=11
x = 210/10 = 21

Question 6: What number must be subtracted from the numerator and denominator 43/37 that it becomes 3 : 2 ?
Solution: Let x be the number subtracted from the fraction.
(43 – x) / (37 – x) = 3/2
86 – 2x = 111 – 3x
x = 25

Question 7: A & B start a business with Rs 5000 and Rs 4500. After 4 months A withdraw half of his capital and B withdraw half capital after 6 months and C joins the business with a capital of Rs 7000 after 6 months. Find the profit sharing ratio?
Solution: A invest 5000 for 4 months and withdraw half amount after 4 months so next 8 months A’s investment is 2500.
B invest 4500 and after 6 month he withdraw half of his capital and next 6 month only half.

             A                 B                C
             5000x4         4500x6              7000x6      
             2500x8         2250x6
Total =      40000         40500               42000                 
Ratio=        80       :     81        :        84

Question 8: A, B, C start a business, A invest money for 4 months and claim 1/8 of the total profit & B invest money for 6 months & claim 1/3 of the profit while C invest Rs. 1560 for 8 months. How much money A & B invest?
Solution: A and B claims 1/8 and 1/3 So take LCM (1/8, 1/3) =24
A’s profit 3 and B’s profit 8
Remaining profit of C =24 – 3 – 8 = 13

   
                   A                 B                     C
Profit ratio       3                 8                     13
Time ratio         2                 3                     4
Capital=P/T     (3/2)*12=18     (8/3)*12=32           (13/4)* 12                     (12 months)

C’s capital is given 39 unit = 1560
1 unit = 40
A invest =18 x 40 = 720
B invest = 32 x 40 = 1280

Question 9: Two friends rent a croft for 10 months.First one puts in 100 horse for 8 months. How many horse can second one put in for the remaining two months. If second one pays half as much as first.
Solution: Let Second one can put x horse in the croft.
A : B = 1 : 1/2
A : B = 2 : 1
(100 * 8) /( x * 2) = 2
4x = 800
x=200 horse

Question 10: A and B started a business with Rs 5000 and 2000. If A is working partner and takes 20% of the total profit as his salary and remaining profit is divided according to their capital. If in this process A received Rs 3800 more than B .Find the amount of total profit?
Solution: A’s profit is 20% of total profit= 1x/5x
Remaining profit = 5x – 1x =4x
Let it be distributed in between A and B acc. to their capital.

                       A              B
Capital               5000           2000
Ratio                  5       :      2
                      4x * 5/7      4x * 2/7
                      20x/7          8x/7

A’s profit = x + 20x/7 = 27x / 7
B’s profit= 8x/ 7
A receive 3800 more than B
Then 27x/7 – 8x/7 = 19x/7
19x/7 = 3800
x= 1400
Total profit = 1400 x 5 = Rs 7000.

Question 11: Ram puts Rs. 375 more in a business than Shaym. Ram invest for 8 months while Shyam invest for 4 months. If the total share of Ram is 75 more than that of Shyam out of total profit of Rs. 125. Find the capital invest by Ram?
Solution: Let x is the share of Shyam
Than Ram’s share= x +75
Total profit = 125
x + 75 + x =125
x =25
Ram’s profit = 100 and Shyam’s profit = 25

               Ram           Shyam
Time ratio      2       :       1
Profit ratio    4       :       1
Capital=P/T     2       :       1

Ram invest 375 more than Shyam
So, 2 – 1 = 1 unit -> 375
Ram’s capital = 750