Question

    A certain number of persons can dig a trench 100 m long, 50 m broad and 10 m deep in 10 days. The twice number of persons can dig another trench 20 m broad and 15 m deep in 30 days. The length of the second trench is?

Answer 1

Hi there!

Let the required length be x metres.

More breadth, Less length (Indirect Proportion)

More depth, Less length (Indirect Proportion)

More days, More length (Direct Proportion)

Breadth 20 : 50] : : 100 : x

Depth 15 : 10] : : 100 : x

Days 10 : 30] : : 100 : x

∴ 20 × 15 × 10 × x = 50 × 10 × 30 × 100

x = 50 × 10 × 30 × 100/20 × 15 × 10

x = 500 m

Hence,
The length of second trench is 500 m.

[ Thank you! for asking the question. ]
Hope it helps!

Answer 2

Answer:

500 m

Step-by-step explanation:

Given : A certain number of persons can dig a trench 100 m long, 50 m broad and 10 m deep in 10 days.

The twice number of persons can dig another trench 20 m broad and 15 m deep in 30 days

To Find : The length of the second trench is?

Solution:

Let the required length be x meters.

More breadth, Less length (Indirect Proportion)

More depth, Less length (Indirect Proportion)

More days, More length (Direct Proportion)

Breadth  $20 : 50 : : 100 : x$

Depth$15 : 10 : : 100 : x$

Days $10 : 30 : : 100 : x$

$20 \times 15 \times 10 \times x = 50\times  10 \times 30\times 100$

$x = \frac{50\times  10 \times 30\times 100}{20 \times 15 \times 10 }$

$x = 500$

Hence The length of the second trench is 500 m