1) A: B: C is in the ratio of 3: 2: 5. How much money will C get out of Rs 1260?

252

125

503

None of these

Answer: D

Explanation:

C's share = [C's ratio/ sum of ratios] * total amount
C's share = (5/10) * 1260
C's share = 630

2) If a: b is 3: 4 and b: c is 2: 5. Find a: b: c.

3: 2: 5

3: 6: 5

3: 4:10

2: 3: 4

Answer: C

Explanation:

The ratio of a: b is 3: 4
The ratio of b: c is 2: 5

Note: To find the ratio in such questions, multiply a to b, then b to b, and then b to c.

a: b: c = 3*2: 4*2: 4*5
a: b: c = 6: 8: 20
So, a: b: c = 3: 4: 10

3) A: B is 1: 2; B: C is 3: 2 and C: D is 1:3. Find A: B: C: D.

3: 6: 4: 12

2: 3: 5: 7

3: 5: 7: 6

2: 1: 6: 13

Answer: A

Explanation:

ATQ,
A: B = 1: 2........... (i)
B: C = 3: 2...........(ii)
C: D = 1: 3.......... (iii)
Now,
Find A: B: C: D
Step 1, A: B: C: D
1: 2 (A: B value by equation i)

Note: To understand the shortcut, remember you need to make the right-hand side missing numbers the same as that of last given number, and for the left-hand side the same is done.

i.e., C: D will contain 2: 2 because 2 is the last number on the right side.

Or, A: B: C: D
1: 2: 2: 2
3: 3: 2: 2 (B: C value by equation ii)
1: 1: 1: 3 (C: D value by equation iii)

Now, multiply vertically and get A: B: C: D.

So, A: B: C: D = (1*3*1): (2*3*1): (2*2*1): (2*2*3)
Or, A: B: C: D = 3: 6: 4: 12

4) 5600 is to be divided into A, B, C, and D in such a way that the ratio of share of A: B is 1: 2, B: C is 3: 1, and C: D is 2: 3. Find the sum of (A and C) and (B and C).

Rs 2400, Rs 3000

Rs 2000, Rs 3000

Rs 2400, Rs 3200

Rs 2000, Rs 3200

Answer: D

Explanation:

ATQ,
A: B = 1: 2........... (i)
B: C = 3: 1........... (ii)
C: D = 2: 3...........(iii)
Now,
Find A: B: C: D
Step 1: A: B: C: D
1: 2 (A: B value by equation i)

Note: To understand the shortcut, remember you need to make the right-hand side missing numbers the same as that of last given number, and for the right-hand side the same is done.

i.e., C: D will contain 2: 2 because 2 is the last number on the right side.

Or, A: B: C: D
1: 2: 2: 2
3: 3: 1: 1 (B: C value by equation ii)
2: 2: 2: 3 (C: D value by equation iii)

Now, multiply vertically and to get A: B: C: D.

So, A: B: C: D = (1*3*2): (2*3*2): (2*1*2): (2*1*3)
= 6: 12: 4: 6
= 3: 6: 2: 3

Now, the share of A and C = [(A+C)/ (A+B+C+D)] * total amount
Or, the share of A and C = [(3+2)/ (3+6+2+3)] * 5600
Or the share of A and C = (5/14)*5600 = 2000
Similarly, the share of B and C = (8/14)*5600 = 3200

Solution 2:

Find A: B: C: D
1: 2: 2: 2
3: 3: 1: 1
2: 2: 2: 3

Now, multiply vertically and get A: B: C: D.

So, A: B: C: D = (1*3*2): (2*3*2): (2*1*2): (2*1*3)
Or, A: B: C: D = 6: 12: 4: 6
Or, A: B: C: D = 3: 6: 2: 3

Sum of the ratios = 3+6+2+3 = 14, but ATQ, it is 5600 Rs.
i.e., 14 * 400 = 5600
So, multiply each and every ratio by 400 and get the share of each:
3*400: 6*400: 2*400: 3*400
So, the share of A = 1200
The share of B = 2400
The share of C = 800
The share of D = 1200

Now, the share of (A+C) = 1200+800 = 2000
The share of (B+C) = 2400+ 800 = 3200

5) The ratio of the total amount distributed in all the males and females as salary is 6: 5. The ratio of the salary of each male and female is 2: 3. Find the ratio of the no. of males and females.

5:9

5:7

7:5

9:5

Answer: D

Explanation:

The total salary of males: the total salary of females = 6:5
The salary of each male: salary of each female = 2:3

To find the number of men and women, divide the total salary of males and females by salary of each male and female.
i.e., 6/2: 5/3
Or, 18: 10 = 9: 5
So, the ratio of the number of males and females = 9:5