25. Three friends divide Rs.624 among themselves in the ratio $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}$. The share of the third friend is :
a. Rs.288
b. Rs.192
c. Rs.148
d. Rs.144

Answer: D

Explanation:
Multiplying the entire ratio by 12 we get,
Ratio = $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}$ = 6:4:3
Share of third friend = Rs.$\left( {624 \times \displaystyle\frac{3}{{13}}} \right)$
= Rs.144

26. One year ago the ratio between Laxman's and Gopal's salary was 3:4. The ratio's of their individual salaries between last year's and this year's salaries are 4:5 and 2:3 respectively. At present the total of their salary is Rs.4290. The salary of Laxman now is :
a. Rs.1040
b. Rs.1650
c. Rs.2560
d. Rs.3120

Answer: B

Explanation:
Let the salaries of Laxman and Gopal one yer before be 12x and 16x.
Given that laxman's last year and present year salary are in the ratio 4 : 5 so his present salary = 5/4(12x) = 15x
Also Gopal's last year and present year salary are in the ratio 2 : 3 so his present salary = 3/2(16x) = 24x
But given that sum of the salaries 15x + 24x = 39x = 4290 $ \Rightarrow $ x = 110
Laxman's present salary = 15x = 15 x 110 = 1650

27. Students in Class I, II and III of a school are in the ratio of 3 : 5 : 8. Had 15 more students admitted to each class, the ratio would have become 6 : 8 : 11. How many total students were there in the beginning?
a. 112
b. 64
c. 96
d. 80

Answer: D

Explanation:
Increase in ratio for 3 classes is 6 - 3 = 8 - 5 = 11 - 8 = 3.
Given, 15 more students are admitted to each class.
Therefore, 3 :: 15 $ \Rightarrow $ 1 :: 5
Therefore, 3 + 5 + 8 = 16 :: 16 x 5 = 80.
Hence, total students in the beginning were 80.

28. A spends 90% of his salary and B spends 85% of his salary. But savings of both are equal. Find the income of B, if sum of their incomes is Rs. 5000.
a. 2000
b. 2400
c. 2125
d. 2400

Answer: A

Explanation:
Let the incomes of A and B are x, y respectively.
Savings of A = (100 - 90)% (x) = 10% (x)
Savings of B = (100 - 85)% (y) = 15% (y)
Given, both saves equal amount.
Therefore, 10% (x) = 15% (y) $ \Rightarrow \dfrac{x}{y} = \frac{{15\% }}{{10\% }} = \dfrac{3}{2}$
Therefore, x : y = 3 : 2
Hence, B's salary = $\dfrac{{\rm{2}}}{{(2 + 3)}}$ x 5000 = Rs. 2000.

29. A man has some hens and some cows. If the number of heads is 50 and number of feet is 142. The number of cows is:
a. 26
b. 24
c. 21
d. 20

Answer: C

Explanation:
Let the mans has $x$ hens and $y$ cows.
Then total heads = $ x + y = 50 $ - - - (1)
total feet = $2x + 4y = 142$ - - - (2)
Solving above two equations, we get x = 29, y = 21
So cows are 21.

Alternative method:
Let, the man has hens only.
Then total heads = 50 x 1 = 50.
And, legs = 50 x 2 = 100 which is short by 42 from the actual legs i.e. = 142.
Now, replacement of one cow with one hen means same number of heads and two more legs.
Therefore, Hens replaced with cows = $\displaystyle\frac{{{\rm{42}}}}{{\rm{2}}}$ = 21
Therefore, Cows = 21

30. A sum of Rs. 350 made up of 110 coins, which are of either Rs. 1 or Rs. 5 denomination. How many coins are of Rs. 5?
a. 52
b. 60
c. 62

d. 72

Answer: B

Explanation:
Let, the number of Rs.1 coins are x and Rs.5 coins are y.
Then x + y = 110
x + 5y = 350
Solving above two equations, we get y = 60. So number of Rs.5 coins are 60.

Alternative method:
Let, all the coins are of Re. 1 denomination.
Then, total value of 110 coins = 110 x 1 = Rs. 110 which is short from Rs. 350 by Rs. 350 - Rs. 110 = Rs. 240.
Now, replacing 1 one-rupee coin with five-rupee coin mean Rs. 4 extra.
Therefore, Five rupee coins = $\displaystyle\frac{{{\rm{240}}}}{{\rm{4}}}$ = 60 coins

31. The population of a village is 10000. In one year, male population increase by 6% and female population by 4%. If population at the end of the year is 10520, find size of male population in the village (originally).
a. 6000
b. 4800
c. 5200
d. 5600

Answer: A

Explanation:
Let the males are x. Then females are 10000 - x.
Now $x \times 106\% + (10000 - x)104\% = 10520$
$ \Rightarrow x \times \dfrac{{106}}{{100}} + (10000 - x)\dfrac{{104}}{{100}} = 10520$
$ \Rightarrow x \times \dfrac{{106}}{{100}} - x \times \dfrac{{104}}{{100}} + \dfrac{{104}}{{100}}(10000) = 10520$
$ \Rightarrow x \times \dfrac{2}{{100}} + 10400 = 10520$
$ \Rightarrow x = 120 \times \dfrac{{100}}{2}$
$ \Rightarrow x = 6000$

Alternative Method:
Let, the population consists of females only.
Then, increase in the population is 4% of 10000 = 400
Therefore, Increased population = 10000 + 400 = 10400
But, actual increased population = 10520
Difference = 10520 - 10400 = 120
We know that for every 100 people, males grow at the rate of 6 and females at the rate of 4. So Males grow 2 people more than females. But we need 120 people extra. So
Therefore, Male population = $\displaystyle\frac{{{\rm{120}}}}{{\rm{2}}}$ x 100 = 6000

32. A mixture of 55 litres contains milk and water in the ratio of 7 : 4. How many litres of milk and water each must be added to the mixture to make the ratio 3 : 2?
a. 8
b. 9
c. 10
d. 11

Answer: C

Explanation:
Let milk and water in the mixture are 7x and the 4x litre respectively.
Then, 7x + 4x = 55
Therefore, x = $\displaystyle\frac{{{\rm{55}}}}{{{\rm{11}}}}$ = 5
So milk = 35, water = 20
Let k liters of milk and water to be added to the mixture to make to 7 : 4.
$\dfrac{{35 + k}}{{20 + k}} = \dfrac{3}{2}$
$ \Rightarrow $ (35 + k) × 2 = (20 + k) × 3
$ \Rightarrow $ k = 10 liters

33. Three friends divide Rs.624 among themselves in the ratio $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}$. The share of the third friend is :
a. Rs.338
b. Rs.192
c. Rs.148
d. Rs.144

Answer: D

Explanation:
Multiplying the entire ratio by 12 we get,
Ratio = $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}$ = 6:4:3
Share of third friend = Rs.$\left( {624 \times \displaystyle\frac{3}{{13}}} \right)$
= Rs.144