Ratio and Proportion Aptitude Test Paper 4

16) Rs 7800 are distributed among A, B, and C. The share of "A" is the ¾ of the share of B, and the share of B is the 2/3 of the share of C. Find the difference between the share of B and C.

1200
1300
1500
800

Answer: A

Explanation:

The share of A: B is 3: 4
The share of B: C is 2: 3

Note: Whenever such form is given, multiply a to b, then b to b, and then b to c.

i.e., A: B: C = 3*2: 4*2: 4*3
Or, A: B: C = 6: 8: 12
Or, A: B: C = 3: 4: 6
Sun of ratios = 13
Now, the share of B = [4/13] * 7800 = 2400
Share of C = [6/13]* 7800 = 3600

The difference between the share of B and C = 3600- 2400 = 1200

17) A bag contains Rs 410 in the form of Rs 5, Rs 2, and Rs 1 coins. The number of coins is in the ratio 4: 6: 9. So, find the number of 2 Rupees coins.

Answer: C

Explanation:

ATQ, if the ratio of coins = 4: 6: 9
That means if Rs 5 coins are 4, Rs 2 coins are 6, and then Rs 1 coins are 9.

According to the given ratio, the ratio of amounts = 5*4: 6*2: 9*1 = 20: 12: 9
The sum of the ratios of the amounts = 20+12+9 = Rs 41
But ATQ, it is Rs 410, which means multiply each ratio by 10
i.e., new ratio = 40: 60: 90
Now, 40*5: 60*2: 90*1 = 200: 120: 90

The total amount in the form of two rupees coins = 120
So, the two rupees coins = 120/2= 60

18) The ratio of copper and zinc in a 63 kg alloy is 4: 3. Some amount of copper is extracted from the alloy, and the ratio becomes 10: 9. How much copper is extracted?

8kg
6kg
12kg
10kg

Answer: B

Explanation:

Amount of copper in alloy = [copper ratio/ sum of ratios]* total quantity of alloy

Copper = {4/7}* 63 = 36 kg
Similarly, the amount of zinc in alloy = [3/7] * 63 = 27 kg
Let the extracted copper from alloy = x kg
Remaining copper in alloy = 36-x
The new ratio = 10: 9
i.e., 36-x: 27 = 10: 9
36-x: 3 = 10: 1
36-x = 10* 3
36-x = 30
x = 36-30 = 6 kg.
Hence, the extracted amount of copper is 6 kg.

19) The ratio of land and water on earth is 1: 2. In the northern hemisphere, the ratio is 2: 3. What is the ratio in the southern hemisphere?

1:11
2:11
3:11
4:11

Answer: D

Explanation:

The ratio of land: water = 1: 2
In the northern hemisphere the ration of land: water = 2: 3

Note: Earth is divided equally into two hemispheres called northern hemisphere and southern hemisphere.

i.e., the northern hemisphere is 50% of the total earth.

We can say southern hemisphere = total area- northern hemisphere.

To make the northern hemisphere 50% of the total area
Multiply the ratio of the earth by 10 and northern hemisphere by 3
Now, earth's ratio Land: water = 1*10: 2*10 = 10: 20............... (i)
Northern hemisphere's ratio = 2*3: 3*3 = 6: 9...................... (ii)

Subtract equation i by ii

Hence, southern hemisphere = 10- 6: 20-9 = 4: 11

20) Vessels A and B contain mixtures of milk and water in the ratios 4: 5and 5: 1respectively. In what ratio should quantities of the mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5: 4?

2: 5
4: 3
5: 2
2: 3

Answer: C

Explanation:

Let the quantity of vessels A and B in the ratio x: y to form a mixture of water and milk in the ratio 4: 5.
Or, Milk: water = 5: 4.
From vessel A, milk: water = 4x/9: 5x/9
From vessel B, milk: water = 5y/6: 1y/6

Now, ATQ quantities of the mixture should be taken from A and B.
Ratio of milk: water = [4x/9 +5y/6]: [5x/9+ 1y/6] = 5/4
Take the LCM of 9 and 6 = 54
Or, [24x + 45y]/54: [30x+9y]/54 = 5/4
Or, [8x + 15 y]: [10x + 3y] = 5/4
Or, [8x + 15y] * 4 = [10x + 3y] * 5
Or, (60-15) y = (50-32) x
Or, 45y = 18x
Or, 5y = 2x
Or, x: y = 5: 2
Hence, the quantity of mixture should be taken from A and B in the ratio 5: 2.