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11. If A : B = 2 : 3, B : C = 4 : 5 and C : D = 5 : 9 then A : D is equal to:

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Solution:
AD=AB×BC×CD=23×45×59=2×4×53×5×9=827=8:27
12. In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is

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Solution:
Girls : boys = 6 : 5
Hence, girls = 6×6611  = 36
Boys = 30
New ratio, 30 : (36 + 4) = 3 : 4
13. What must be added to each term of the ratio 7 : 11, So as to make it equal to 3 : 4?

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Solution:
Let x be added to each term.According to question,7+x11+x=34Or,33+3x=28+4xOr,x=5
14. Two numbers are in ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. The smaller number is

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Solution:
Let the numbers be 7x and 11x.
According to question,7x+711x+7=23Or,22x+14=21x+21Or,x=7Smallernumber=49
15. Two numbers are in ratio P : Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to RS. again, when 1 is added to both the numerator and denominator, it becomes 12. Find the sum of P and Q.

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Solution:
If we go through normal method, It will be quite cumbersome,so,
We will solve this question through options

Taking Option A:
It has P + Q = 3.
The possible value of PQ is 12 or 21
Using 12, we see that on adding 2 in both the numerator and denominator we get 34 (not required value)
Similarly we check for 21, this will also not give the required value

Option B:
We have 13 possible ratio
Then, we get the final value as 35 (not = to 12)
Hence, rejected

Option C:
Here we have 14 or 23
Checking for 14 we get 36 = 12
Hence, the option c is correct
16. The ratio of water and milk in a 30 liter mixture is 7 : 3. Find the quantity of water to be added to the mixture in order to make this ratio 6 : 1.

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Solution:
Here,Let water = 7x and milk = 3x
Now,
7x + 3x = 30
x = 3
So, water = 7x = 7 × 3 = 21 liter
Milk = 3x = 3 × 3 = 9 liter

Now, we keep milk constant and add water to mixture to get ratio 6 : 1
Let water in this mixture = 6y and milk = y
We have, milk = 9 liter, so y = 9 liter
Water = 6y = 6 × 9 = 54 liter
Then extra water to be added is 33 liter
17. The incomes of A and B are in the ratio 3 : 2 and their expenditure are in ratio 5 : 3. If each saves Rs. 1000, then, A's income can be:

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Solution:
Let income of A and B be 3x and 2x respectively. Also, their expenditure is 5y and 3y.

Now, according to question,
3x - 5y = 1000 ------- (i) × 3
2x - 3y = 1000 ---------- (ii) × 5
9x - 15y - 10x + 15y = 3000 - 5000
Or, -x = -2000
Or, x = 2000
Then, income of A = 3x = 3 × 2000 = Rs. 6000
18. The difference between two positive numbers is 10 and the ratio between them is 5 : 3. Find the product of the two numbers.

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Solution:
Let the two positive numbers be 5x and 3x respectively
According to question,
5x - 3x = 10
Or, x = 5
Then numbers are 25 and 15
Thus, their product = 25 × 15 = 375
19. If 30 oxen can plough 17 th of a field in 2 days, how many days 18 oxen will take to do the remaining work?

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Solution:
We will use work equivalence method,
3018=1767×x253=16×x2Or,x=603=20days
20. A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?

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Solution:
Given;
3dog = 4 cat
Or, dogcat=43
Let cat's 1 leap = 3 meter and dogs 1 leap = 4 meter
Then, ratio of speed of cat and dog = 3×54×4  = 15 : 16

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