Given that First heater boils certain amount of water in 15 minutes.
Another heater boils it in 10 minutes.
Let water boiled by both of them in one minute be 1 / x
Amount boiled by first heater in 1 minute = 1 / 15
Water boiled by another heater = 1 / 10
so the equation forms in this way :
1 / 15 + 1 / 10 = 1 / x
L.C.M = 30
1 × 2 / 15 × 2 + 3 × 1 / 10 × 3 = 1 / x
2 + 3 / 30 = 1 / x
5 / 30 = 1 / x
Cross multiply the fractions
5 × x = 1 × 30
5x = 30
x = 30 / 5
x = 6
So time taken by both the heaters to boil the water is 6 minutes.
So the answer is 6 minutes.
