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**Hint:**We must first assume a variable (say $x$) that depicts the rate at which fluid flows from one pipe. We can then use the information that 4 pipes take 70 minutes to fill the tank, to find the volume of the tank. We will again have to assume a variable (say $t$) that is the time taken to fill the tank by 7 pipes. Hence, by equating the volume in two cases, we can find the value of variable $t$.

**Complete step-by-step solution:**

Let us assume that a pipe can fill $x$ litres in 1 minute, that is, $x$ litres per minute.

So, we can say that 4 pipes can fill $4x$ litres in 1 minute, that is, $4x$ litres per minute.

We are given that 4 pipes take 70 minutes to fill the tank.

So, we can easily write that in 70 minutes, 4 pipes will fill = $70\times 4x$ litres.

Thus, we can say that the total volume of the tank = $280x$ litres.

Now, since we know that 1 pipe fills $x$ litres per minute, so we can very well say that 7 pipes will fill the tank at the rate of $7x$ litres per minute.

Again, let us assume that the time taken to fill the tank by 7 pipes is $t$ minutes.

So, we can say that in $t$ minutes, 7 pipes will fill = $7xt$ litres.

But we had assumed that in $t$ minutes, the tank is completely filled. So, $7xt$ litres must be equal to the volume of the tank, which is $280x$ litres.

Thus, we can write

$7xt=280x$

Cancelling the terms from both sides, we get

$t=40$ minutes.

**Hence, we can say that 7 pipes can fill the tank in 40 minutes.**

**Note:**We can also solve this problem without having to assume any extra variable, using the following approach. We know that 4 pipes can fill the tank in 70 minutes. So, we can say that 1 pipe will tank in $70\times 4=280$ minutes. And thus, 7 pipes can fill the tank in $\dfrac{280}{7}=40$ minutes.

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