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QUESTION: 1

A and B together has Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?

Solution:

QUESTION: 2

Two numbers are 20% and 50% more than "the third number respectively". The ratio of the two numbers is:

Solution:

Let the third number be x.

Then, first number = 120% of

Second number = 150% of

∴ Ratio of first two numbers

QUESTION: 3

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

Solution:

Let the shares of A, B, C and D be Rs. 5*x*, Rs. 2*x*, Rs. 4*x* and Rs. 3*x* respectively.

Then, 4*x* - 3*x* = 1000

⇒ *x* = 1000.

∴ B's share = Rs. 2*x* = Rs. (2 x 1000) = Rs. 2000.

QUESTION: 4

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

Solution:

Originally, let the number of seats for Mathematics. Physics and Biology be 5x. 7x and 8x respectively.

Number of increased seats are (140% of 5x). (150% of 7x) and (175% of 8x).

QUESTION: 5

In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

Solution:

Quantity of milk

Quantity of water in it = (60 - 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres

Then, milk : water

∴ Quantity of water to be added = 60 litres.

QUESTION: 6

Find the ratio A : B : C : D If,

A : B = 3 : 5

B : C = 5 : 7

C : D = 9 : 11

Solution:

A : B = 3 : 5

B : C = 5 : 7

C : D = 9 : 11

A : B : C : D = 3 x 5 x 9 : 5 x 5 x 9 : 5 x 7 x 9 : 5 x 7 x 11

5 can be taken away as it is common in all.

27 : 45 : 63 : 77

The required ratio A : B : C : D is 27 : 45 : 63 : 77.

QUESTION: 7

Find the ratio A : B : C : D : E if,

A : B = 4 : 5

B : C = 6 : 7

C : D = 9 : 10

D : E = 5 : 2

Solution:

A : B = 4 : 5

B : C = 6 : 7

C : D = 9 : 10

D : E = 5 : 2

A : B : C : D : E = 4 x 6 x 9 x 5 : 5 x 6 x 9 x 5: 5 x 7 x 9 x 5: 5 x 7 x 10 x 5: 5 x 7 x 10 x 2

216 : 270 : 315 : 350 : 140

The required ratio A : B : C : D : E is 216 : 270 : 315 : 350 : 140

QUESTION: 8

If 4 : 8 : C are in continued proportion then find C?

Solution:

We know that if a, b and c are in continued proportion,

then b^{2} = ac

8^{2} = 4.C

C = 64/4 = 16

QUESTION: 9

11 : b : 44 are in continued proportion. Find b.

Solution:

We know that if a, b and c are in continued proportion then b^{2} = ac

b^{2} = 11.44

b^{2} = 484

b = 22

QUESTION: 10

The annual income of Victor and Angela are in the ratio 8 : 3 and their annual expenditures are in the ratio 4 : 1. If each save Rs. 2000 per annum. What is the annual expense of Angela?

Solution:

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