Question

If 30 men can build a wall in 15 days, how many men will be required to build the wall in 10 days​

Answer 1

no. of men to build a wall in 15 days=30 men

no. of men to build a wall in 1 day = 30/15

no. lf men to build a wall in 10 days = 30/15×10=20 men

i hope this will help you!

Answer 2

$\underline{\underline{\sf{\green{Question:}}}}$

If 30 men can build α wαll in 15 dαys, how mαny men will be required to build the wαll in 10 dαys?

$\underline{\underline{\sf{\green{Required\;Solution:}}}}$

30 men can build α wαll in 15 dαys. We hαve to find the number of men required to build α wαll in 10 dαys.

The number of men αnd dαys tαken to build the wαll αre in inverse proportion.

Lets αssume the number of men αs 'x' to complete build the wαll in 10 dαys.

No. of men                    No. of dαys

30                                          15

x                                             10

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⇒ $\sf 10x=15 \times 30$

⇒ $\sf 10x=450$

$⇒ ~\sf x = \dfrac{\cancel {450}}{\cancel {10}}$

$\therefore \boxed{\orange{\sf x = 45}}$

Finαl αηswεr: 45 men will be required to build the wall in 10 dαys

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Let's memorize:

Proportion ↓

Proportion tells us about a portion or part in relation to a whole.

Direct proportion ↓

A proportion of two variable quantities when the ratio of the quantities is constant.

Eg. Look at the circles, in the attachment. We see divisions of a circle made by its diameters.

In figure (A) one diameter makes 2 parts of the circle.

In figure (B) two diameters make 4 parts of the circle.

In figure (D) four diameters make 8 parts of the circle.

$\sf \dfrac{No.\; of\; diameters}{No.\; of\; divisions} = \dfrac{1}{2} = \dfrac{2}{4} = \dfrac{3}{6} = \dfrac{4}{8}$

Here, the ratio of the number of diameters  to the number of divisions remains constant.

Inverse proportion

A relation between two quantities such that one increases in proportion, as the other one decreases

Eg. Some volunteers have gathered to dig 90 pits for  a tree plantation programme. One volunteer digs one  pit in one day. If there are 15 volunteers, they will  take  $\sf \dfrac{90}{15} = 6 ~days~ to~ dig~ the ~pits.$

10 volunteers will take  $\sf \dfrac{90}{ 10} = 9 ~days.$

Are the number of pits and the number of volunteers  in direct proportion?  If the number of volunteers decreases, more days are required; and if the number  of volunteers increases, fewer days are required for the job. However, the product  of the number of days and number of volunteers remains constant. We say that  these numbers are in inverse proportion.

◾️ Suppose Sudha has to solve 48 problems in a problem set. If she solves

1 problem every day, she will need 48 days to complete the set. But, if she solves  8 problems every day, she will complete the set in $\sf \dfrac{48}{8}$ = 6 days and if she solves  12 problems a day, she will need   = 4 days. The number of $\sf \dfrac{48}{12}$ problems solved  in a day and the number of days needed are in inverse proportion. Their product  is constant.

Thus, note that 8 × 6 = 12 × 4 = 48 × 1

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Hope it helps! :)