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P

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Rama Krishna replied | 09/12/2016

5:7 here 7-5=2 parts and 3:4 here 4-3= 1 parts
so 1 parts equal to parts 2 * (3:4)= 6:8
1 subtracted from each part.

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Abhishek replied | 10/12/2016

it will be like suppose x is the no
then
(5-x)/(7-x) = 3/4.
By solving we got x = -1.
Hence, 1 should be added to get the answer.

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V

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Rishikesh replied | 08/12/2016

1.2.

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Abhishek replied | 10/12/2016

1.2.

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S

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P

Pooja replied | 29/11/2016

49:9.

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Sarvajeet replied | 06/12/2016

49:9.

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B

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Kundan replied | 10/12/2016

Square root of the product of both the numbers.

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Rajendran replied | 11/12/2016

Mean proportion of 25, 64 = square root (25 * 64)
= square root of (1600)
= 40.

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A

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Rajendran replied | 24/11/2016

Given that x : y = 9 : 10.
(x/y) = (9/10).
now (5x + 3y) : (5x - 3y) = ?
Dividing both Nr and Dr by y we (5x/y + 3y/y)/5(x/y) - 3(y/y)
= [5(x/y) + 3]/[5(x/y) - 3(y/y)]
= [5(9/10) + 3]/5(9/10) - 3]
=[(45/10) + 3]/[(45/10) - 3].
taking LCM on Nr. and Dr., we get:-
=[(45 + 30)/10]/(45 - 30)/10
= (75/10)/(15/10)
= (75/10) * (10/15)
=75/15
=...  more»
Given that x : y = 9 : 10.
(x/y) = (9/10).
now (5x + 3y) : (5x - 3y) = ?
Dividing both Nr and Dr by y we (5x/y + 3y/y)/5(x/y) - 3(y/y)
= [5(x/y) + 3]/[5(x/y) - 3(y/y)]
= [5(9/10) + 3]/5(9/10) - 3]
=[(45/10) + 3]/[(45/10) - 3].
taking LCM on Nr. and Dr., we get:-
=[(45 + 30)/10]/(45 - 30)/10
= (75/10)/(15/10)
= (75/10) * (10/15)
=75/15
= 5.
Therefore (5x +3y) : (5x - 3y) = 5 : 1. «less

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Sarvajeet replied | 06/12/2016

5:1.

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S

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Ram Mohan replied | 28/11/2016

Given that A:B = 4:5, B:C = 6:7 and C:D = 14:15.
Therefore, A/B =4/5; B/A = 6/7; C/D = 14/15 We can write A/D as A/D = A/B * B/C *C/D = 4/5 * 6/7 * 14/15 = 16/25
Thus, A : D = 16 : 25.

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Sarvajeet replied | 06/12/2016

16:25.

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T

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Shikha replied | 23/11/2016

4:5.

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Ram Mohan replied | 23/11/2016

The ratio of the two Numbers is 4:5.
If the third Number is 100, then the First number is 120 and the Second number is 150.
Their ratio = 120 : 150 = 4 : 5.

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R

Ramya 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

Two numbers are in the ratio of 5 : 3, if 8 is added to each number, the ratio becomes 2 : 3. Find the numbers?

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Sarvajeet replied | 26/11/2016

-40/9, -8/3

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Tapas replied | 26/11/2016

Let the numbers are x and y.
So, by the given condition:
x/y = 5/3 --> 3x = 5y ........ (1)
and
(x+8)/(y+8)=2/3 --> 3(x+8) = 2(y+8) --> 3x + 24 = 2y + 16 --> 3x - 2y = -8 .......(2)
Combining (1) and (2): 5y - 2y = -8 --> 3y = -8 --> y = -8/3
From (1): x = 5y/3 = -40/9
Answer: x = - 40/9, y = - 8/3.

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M

Momin 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

If (4a + 9b) : (4c + 9d) = (4a - 9b) : (4c - 9d), show that a : b = c : d?

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Mamata replied | 27/11/2016

(4a+9b)(4c-9d)= (4c+9d)(4a-9b)
16ac-36ad+36bc-81bd)= 16ac-36bc+36ad-81bd)
-72ad=-72bc
ad=bc
a/b=c/d
a:b=c:d.

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Sarvajeet replied | 06/12/2016

(By Componendo and Dividendo) 8a:18b=8c:18d or a:b = c:d.

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S

Sarala 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

If (3a + 4b) / (3c + 4d) = (3a - 4b) / (3c - 4d), prove that a / b = c / d?

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Sachin replied | 27/11/2016

9a:8b=9c:8d (by compnendo and dividendo).

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Mamata replied | 27/11/2016

(3a+4b)(3c-4d)=(3a-4b)(3c+4d)
9ac-12ad+12bc-16bd=9ac+12ad-12bc-16bd
-24ad=-24bc
ad=bc
a/b=c/d.

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V

Vathsala 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20 % and 10 % respectively, what will be the new ratio?

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Rama Krishna replied | 08/12/2016

Let the number of boys = 7k
number of girls = 8k

Due to increase in percentage,

number of boys = 7K*120/100

number of girls = 8K*110/100

New ratio = { 7K*120/100 } : { 8K*110/100 }
Or
7:8 can also be written as 70:80
120/100*70 = 84
110/100*80 = 88
so,new ratio= 84 : 88
or 42 : 44
or 21 : 22
Or
(7x+0.2*7x)/(8x+0.1*8x)=21...  more»
Let the number of boys = 7k
number of girls = 8k

Due to increase in percentage,

number of boys = 7K*120/100

number of girls = 8K*110/100

New ratio = { 7K*120/100 } : { 8K*110/100 }
Or
7:8 can also be written as 70:80
120/100*70 = 84
110/100*80 = 88
so,new ratio= 84 : 88
or 42 : 44
or 21 : 22
Or
(7x+0.2*7x)/(8x+0.1*8x)=21:22. «less

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Ankit replied | 09/12/2016

21/22

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P

Praneeth 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

What must be added to each of 7, 16, 43 and 79 so that they become proportion? Find the number, which are in the proportion?

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Ram Mohan replied | 21/11/2016

Let us suppose, that we have to add 'x', to each of 17,16,43,and 79 so that they are in proportion
Therefore, ( 7 + x ) : (16 + x ) : : ( 43 + x ) : ( 79 + x ), ==> ( 16 + x ) (43 + x ) = (7 + x ) ( 79 + x )
after simplification and solving for ' x' , we get x = 5 .
Verification :
After adding '5' to the given numbers, we get 12, 21, 48, 84 which satisfy 12 :...  more»
Let us suppose, that we have to add 'x', to each of 17,16,43,and 79 so that they are in proportion
Therefore, ( 7 + x ) : (16 + x ) : : ( 43 + x ) : ( 79 + x ), ==> ( 16 + x ) (43 + x ) = (7 + x ) ( 79 + x )
after simplification and solving for ' x' , we get x = 5 .
Verification :
After adding '5' to the given numbers, we get 12, 21, 48, 84 which satisfy 12 : 21 : : 48 : 84 OR 4 : 7 : : 4 : 7 «less

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Sarvajeet replied | 06/12/2016

5.

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K

Kirti 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

What number should be subtracted from each of the numbers 23, 30, 57 and 78, so that the remainders are in the proportion?

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Sarvajeet replied | 06/12/2016

6.

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A

Abraham 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

If x : y : z, show that x : z = (square of x) : (square of y)?

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Shambhavi replied | 07/12/2016

As we know that , x:y:z , this implies that, y^2=x*z.
Simplifying x:z=x^2:y^2, we get, y^2=x*z, which is the same as above. Thus, they are equal.

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H

Hemlata 11/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Ratio and Proportion

The work done by (x - 3) men in (2x + 1) days and the work done by (2x + 1) men in (x + 4) days are in the ratio of 3 : 10. Find the value of x?

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Tapas replied | 27/11/2016

Let the amount of work done by 1 man in 1 day is w.
Then the work done by (x - 3) men in (2x + 1) days = (x - 3)(2x + 1)w.
And the work done by (2x + 1) men in (x + 4) days = (2x + 1)(x + 4)w.
By the given condition,
[(x - 3)(2x + 1)w] / [ (2x + 1)(x + 4)w] = 3 : 10
Simplifying:
(x - 3) / (x + 4) = 3 / 10 --> 10x - 30 = 3x + 12 --> 10x - 3x = 30 + 12 -->...  more»
Let the amount of work done by 1 man in 1 day is w.
Then the work done by (x - 3) men in (2x + 1) days = (x - 3)(2x + 1)w.
And the work done by (2x + 1) men in (x + 4) days = (2x + 1)(x + 4)w.
By the given condition,
[(x - 3)(2x + 1)w] / [ (2x + 1)(x + 4)w] = 3 : 10
Simplifying:
(x - 3) / (x + 4) = 3 / 10 --> 10x - 30 = 3x + 12 --> 10x - 3x = 30 + 12 --> 7x = 42 --> x = 42/7 = 6
Answer: x = 6. «less

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Saurabh replied | 04/12/2016

Always remember a formula for these type of questions where work no. of men and no. of days /working hours are given:-
lhs = rhs
m1 * d1* t1 / work done 1 = m2* d2* t2 / work done 2 here * = multiply and / = divide. m=men d= days
As work done ratio by...  more»
Always remember a formula for these type of questions where work no. of men and no. of days /working hours are given:-
lhs = rhs
m1 * d1* t1 / work done 1 = m2* d2* t2 / work done 2 here * = multiply and / = divide. m=men d= days
As work done ratio by 1 to 2 is 3:10 just put the value (x-3)*(2x+1) /3 = (2x+1)*(x+4) /10.
on solving 10x-30= 3x+12,
7x=42
Therefore x=6. «less

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