Question

Mr Prasad travel one by two of the distance by train ,1 upon 4 by bus,1 upon 4 by auto and the remaining 4 km by foot the total distance travelled by him was

Answer 1

Question:

Mr Prasad travel one by two of the distance by train ,1 upon 4 by bus,1 upon 4 by auto and the remaining 4 km by foot. Find the total distance travelled by him was.

answer:

Total distance travelled by him was  14.22 km approx.

Given:

1/2 part of the distance he travelled by train.

Among the remaining distance_

1/4 part of the distance he travelled by bus.

Among the remaining distance after travelling by bus_

1/4 part of the distance he travelled by auto.

The remaining 4 km he walked on foot.

To find:

Total distance travelled by him.

Explanation:

Let, the total distance be, 'n' km.

The part of the distance travelled by train _

(n× $\frac{1}{2}$)

= $\frac{n}{2}$ parts

The part of the distance travelled by him without train_

(n - $\frac{n}{2}$) parts

= ($\frac{2n-n}{2}$)  [∵ THe L.C.M. of the denominators is 2.]

= $\frac{n}{2}$ parts

∴ The part of the distance travelled by him by bus_

($\frac{n}{2}$×$\frac{1}{4}$)

= $\frac{n}{8}$ parts

After travelling by bus he travelled_

($\frac{n}{2}$ - $\frac{n}{8}$)

=($\frac{4n-n}{8}$) [∵ The L.C.M. of the denominators is 8.]

= $\frac{3n}{8}$ parts of the distance.

∴ He travelled by auto_

($\frac{3n}{8}$ × $\frac{1}{4}$)

= $\frac{3n}{32}$ parts of the distance.

∴ After travelling by auto the part of the distance left_

($\frac{3n}{8}$ - $\frac{3n}{32}$)

=($\frac{12n-3n}{32}$) [∵ The L.C.M. is 32.]

= $\frac{9n}{32}$ parts of the distance.

∴ $\frac{9n}{32}$  parts of the distance he walked on foot.

∴ According to problem:

$\frac{9n}{32}$ = 4

⇒ 9n = (4×32)

⇒ n = $\frac{128}{9}$

⇒ n = 14.22  km approx.

∴ He totally travelled 14.22 km approx.