**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 =** 15**

**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 C5000_{x4}4500_{x6}7000_{x6}2500_{x8}2250_{x6}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 CProfit 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 BCapital 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 ShyamTime 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**

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