# Ratio and Proportion

1**. **An amount of money is to be divided among P, Q and R and in the ratio of 5:11:23 respectively**. **If the difference between the total share of P and Q together and R’s share is Rs**. **2,800 what is the difference between Q and R’s share? [Bank 2000]

**(a) **Rs**. **6,400

**(b) **Rs**. **3,600

**(c) **Rs**. **4,800

**(d) **Rs**. **3,200

**Answer: (c)**

**Explanation:**

Let he shares of P, Q and R be 5x,11x and 23x respectively, by given condition**.**

R-(P+Q) = 2800

23x -16x = 2800

7x =2800

x=400

Difference between Q’s an R’s share = 23x-11x = 12x= Rs**. **4800

2**. **If x : y= 3:1, then [SSC Grad**. **2000]

**(a) **13:14

**(b) **14:13

**(c) **10:11

**(d) **11:10

**Answer: (a)**

**Explanation:**

[ By componendo and dividendo]

(0r)

=13:14

3**. **Consider the following ratio’s 1:72, 17:18, 11:12, the correct sequence in decreasing order is

**(a) **1:72 > 11:18 > 17:18

**(b) **11:18 > 1:72 > 17:18

**(c) **17:18 > 11:12 > 1:72

**(d) **none of the above

**Answer: (c)**

**Explanation:**

Step 1:

204>198

17:18>11:12

Step 2:

1:72 and 11:12

L**.c.m** of 72 and 12

792>12

Therefore, decreasing order is

17:18 > 11:12 > 1:72

4**. **A sum of money is to be distributed among P, Q, and R in the ratio 6:19:7**. **If R gives Rs**. **200 from his share to Q, the ratio of P, Q and R becomes 3:10:3, what is the total sum? [Bank 2000]

**(a) **Rs**. **4800

**(b) **Rs**. **12800

**(c) **Rs**. **3200

**(d) **data inadequate

**Answer: (a)**

**Explanation:**

Let the shares of P, Q and R be 6x, 19x and 7x**.**

By given condition, R’s new share = 7x – 200

Q’s new share = 19x + 200

New ratio = 6x :19x +200:7x-200=3:10:3

P : R = 6x :7x -200=3 :3

6x=7x-200

x=200

Total sum 6x + 19x + 7x = 32x = Rs**. **4800

5**. **A sum of Rs**. **370 is to be divided among A, B and C such that

Then, A’s share (in rupees) is: [SSC Grad**. **1999]

**(a) **240

**(b) **120

**(c) **100

**(d) **90

**Answer: (d)**

**Explanation:**

A**: **B=3:4; B**:**C=3:4

[equating with respect to A]

=Rs**. **90

6**. **The incomes of A, B and C are in the ratio 7:9:12 and their spending are in the ratio 8:9:15**. **If a save , of his income, then the savings of A, B and C are in the ratio: [SSC Grad**. **2003]

**(a) **56:99:69

**(b) **69:56:99

**(c) **99:56:69

**(d) **99:69:56

**Answer: (a)**

**Explanation:**

By given condition, if 7x be the income of A the

savings of B= 9x – 9y =

And savings of C = 12x-15y =

The required ratio =

= 56:99:69.

7**. **By mistake, instead of dividing Rs**. **117 among A, B and C in the ratio it was divided in the ratio of 2:3:4**. **Who gains the most and by how much? [SSC Grad**. **1999]

**(a) **A, Rs**. **28

**(b) **B, Rs**. **3

**(c) **C, Rs**. **20

**(d) **C, Rs**. **25

**Answer: (d)**

**Explanation:**

The correct ratio =

A’s correct share =

B’s correct share =

C’s correct share =

A got =

B got =

C got =

C gained most by (52-27) =Rs**. **25

8**. **The ratio of the first and second class fares between two stations is 3 : 1 and that of the number of passengers travelling between the two stations by the first and the second class is 1 : 50**. **If in a day, Rs**. **1, 325 are collected from the passengers travelling between the two stations, then the amount collected from the second class from the second class passengers is: [SSC Grad**. **2000]

**(a) **Rs**. **1,250

**(b) ** Rs**. **1,000

**(c) **Rs**. **850

**(d) **Rs**. **750

**Answer: (a)**

**Explanation:**

Let the fares be 3x and x respectively for the first and second class**.**

Suppose in a day passengers travelling between the two stations be 1 and 50**.**

Then by given condition, 3x×1+x×50=1,325 => x=25

The amount collected from second class = 25×50 = Rs**. **1250

9**. **Ram, Sanjay and Suresh assemble for a contributory party**. **Ram brings 3 apples while Sanjay brings 5**. **Since Suresh did not have any apples, he contributed Rs**. **8**.**How many rupees should Ram and Sanjay respectively get, assuming each of the three consumes an equal portion of the apples? [Bank 2007]

**(a) **1, 7

**(b) **3, 5

**(c) **5, 3

**(d) **2, 6

**Answer: (a)**

**Explanation:**

Total apples = 8

Each person’s share = apples = apples

Ram’s share =

Sanjay’s share =

Their shares respectively are in the ratio

Ram’s share =

10**. **A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4**. **If they save Rs**. **1800 and Rs**. **1600 respectively, find the monthly income of B** **[SSC Grad**. **2002]

**(a) **Rs**. **3400

**(b) **Rs**. **2700

**(c) **Rs**. **1720

**(d) **Rs**. **7200

**Answer: (d)**

**Explanation:**

Incomes of A and B=5x and 6x and expenses of A and B = 3y and 4y

Then, savings of A = 5x-3y = 1800—?(1)

Savings of B = 6x-4y = 1600—?(2)

By solving equations (1) and (2)

y = 1400

Monthly income of B = Expenses of B + savings of B

= 4y+1600 = 4(1400) + 1600 = Rs**. **7200