1. If a/b = 3 / 2 then find (3a + b ) / (3a - b) =
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Correct Ans:11 / 7
Explanation:
2. If a:b = 1 : 2 and b : c = 3 : 2 then a : b : c =
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Correct Ans:3 : 6 : 4
Explanation:
a : b = 1 : 2
=> Mulitply by "3" on both sides
=> a x 3 : b x 3 =1 x 3 : 2 x 3
=> a : b= 3 : 6
b : c = 3 : 2
=> Mulitply by "2" on both sides
=>b x 2 : c x 2 = 3 x 2: 2 x 2
=> b : c =6 : 4
Now a : b : c =3 : 6 : 4
3. For every 2 chocolate Ram gets Shyam is given 3 chocolate. If the total number of chocolate distributed to them is 65, then find the number of chocolates Shyam received.
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Correct Ans:39
Explanation:
4. The ratio of number of boys and girls in a school of 720 students is 7:5. How many more girls should be admitted to make the ratio 1:1?
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Correct Ans:120
Explanation:
Given, boys : girls = 7 : 5
Let, the total number of boys = 7x and total number of girls= 5x
Given, total students = 720
=> 7x + 5x = 720
=> 12x = 720
=> x = 60
so, total number of boys = 7x = 7 * 60 = 420 and
total number of girls= 5x = 5 * 60 = 300
Let y be the number of girls added to make the ratio 1 : 1
=> 420 / (300 + y) = 1/1
=> 420 = (300 + y)
=> y = 420 - 300
=> y = 120
So, 120 more girls should be admitted to make the ratio 1:1
5. Two numbers are in the ratio 7:9. If 12 is subtracted from each of them, the ratio becomes 3:5. The product of the numbers is:
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Correct Ans:567
Explanation:
Given, ratio of two numbers = 7: 9
Let two numbers be 7x and 9x
If 12 is subtracted from each number,
=> (7x -12) / (9x - 12) = 3/5
=> 5(7x - 12) = 3(9x - 12)
=> 35x - 60 = 27x - 36
=> 8x = 24
=> x = 3
Product of the numbers = 7x * 9x = 7(3) * 9(3) = 21 * 27 = 567
6. If two numbers are in the ratio 6 : 13 and their least common multiple is 312, the sum of the numbers is
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Correct Ans:76
Explanation:
Let the two numbers be 6k and 13k
LCM of 6k and 13k = 78k
=>78k = 312
=> k = 4
Sum of the numbers 6k + 13k = 19k = 19 * 4 = 76
7. The mean proportion between 9 & 36 is:
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Correct Ans:1 8
Explanation:
Mean proportion between a & b = sqrt(a * b)
Mean proportion between 9 & 36 = sqrt (9 * 36)
= sqrt ( 9 * 9 * 4)
= 9 * 2
= 18
8. Ratio between two numbers is 3:2 and their difference is 225, then the smaller number is:
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Correct Ans:450
Explanation:
Given, the ratio of two numbers = 3 : 2
Let the two numbers be 3x and 2x
Given, their difference = 225
=> 3x - 2x = 225
=> x = 225
Smaller number = 2x = 2 * 225 = 450
9. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by
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Correct Ans:One-seventh
Explanation:
When there are 8 people, the share of each person is 1/8 => (Original Share)
When there are 7 people, the share of each person is 1/7
Increase in the share of each person is 1/7 – 1/8 = 1 / 56
1 / 56 ==> Which is 1/7 of 1/8 ==> 1/7 of the original share of each person.
10. If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, then 3 (B + G) is
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Correct Ans:More than 3
Explanation:
Let the number of Boys = x, number of Girls = y;
Given, x/ y = B and y/x = G
Then,
3(B+G) = 3( y/x + x/y)
= 3 (x^2+y^2)/xy > 3
11. Two numbers are in the ratio of 1 : 2. If 7 be added to both, their ratio changes to 3:5. The greater number is
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Correct Ans:28
Explanation:
Let the two numbers be a, b
a/b = 1/2 and
(a+7)/(b+7) = 3/5
=> a= 14 and b = 28
The greater number is 28
12. Radhika purchased one dozen bangles. One day she slipped on the floor fell down. What cannot be the ratio of broken to unbroken bangles?
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Correct Ans:2 : 3
Explanation:
There are totally 12 bangles, sum of the two numbers in the ratio should be a factor of 12,
Only 2:3 does not satisfy the criteria.
13. Rs. 770 have been divided among A, B and C such that A receives two-ninths of what B and C together receive. Then A's share is
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Correct Ans:Rs. 140
Explanation:
A = (2/9) (B+C) A + B + C = 770 (Given)
-----> A + 9A/2 = 770 => 11A = 770 x 2 => A = 70 x 2 = 140
14. Find the triplicate ratio of 3 : 11
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Correct Ans:27 : 1331
Explanation:
15. Two numbers are in the ratio 2:3. If eight is added to both the numbers, the ratio becomes 3:4. The numbers are
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Correct Ans:16 and 24
Explanation:
Let Numbers be m and n,
m/n = 2/3
Adding 8 on both sides,we get
=> (m+8) / (n+8) = 3 / 4
=> 4m + 32 = 3n + 24
By solving each of them seperately we get the value of m , n
=> 4m + 32 =0
=> 4m = 32
=> m = 32 / 4
=> m = 8
3n + 24 = 0
=> 3n = 24
=> n = 24 / 3
=> n = 8
So according to the given ratios,
The numbers are in 2 : 3
m = 8 * 2 = 16
n = 8 * 3 = 24
So m =16 , n = 24
16. If two numbers are in the ratio 6: 13 and their least common multiple is 312, the sum of the numbers is
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Correct Ans:76
Explanation:
Let the two numbers be 6k and 13k
LCM of 6k and 13k = 78k
78k = 312
=> k = 4
Sum of the numbers 6k + 13k = 19k = 19 * 4 = 76
17. If the ratio of number of boys and girls in a class are 3:5 , then which of the following options cannot be the number of students in the class ?
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Correct Ans:81
Explanation:
Ratio of boys and girls = 3:5
Which means the total number of students should be in multiple of 8.
81 is not multiple of 8.
18. One-third of the contents of a container evaporated on the 1st day, three-fourths of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day?
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Correct Ans:One-sixth
Explanation:
After first day, 2/3 rd of the contents remain (i.e., 1 - (1/3) = 2/3)
After second day 2/3 â€“ (3/4) x (2/3) = 1/6 of the content remains
19. Two numbers are in the ratio 3:5, If 8 is subtracted from each, then they are in the ratio 1:3. Then, the second number is:
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Correct Ans:20
Explanation:
Given, ratio of two numbers is 3:5
Let, the two numbers be 3x and 5x.
If 8 is subtracted from each, then
=> (3x - 8) / (5x - 8) = 1/3
=> 3(3x - 8) = (5x - 8)
=> 9x - 24 = 5x - 8
=> 4x = 16
=> x = 4
Second number = 5x = 5 * 4 = 20
20. One-third of the contents of a container evaporated on the 1st day. three-fourths of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day?
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Correct Ans:One - Sixth
Explanation:
After first day, 2/3 rd of the contents remain
After second day 2/3 â€“ (3/4) x (2/3) = 1/6 of the content remains
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