# 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

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

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

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

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

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

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

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

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

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

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

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