Rajat moves 4 5 km towards east from point P to reach point Q. From Q he starts moving 7 9 km towards west to reach point R. What is the distance between points R and Q? How far is Rajat from points P and Q?

Given, Rajat moves towards east from point P to reach point Q = PQ = 4 5 k m Rajat moves towards west from point Q to reach point R = 7 9 k m So, the distance between R and Q is = RQ = 7 9 k m The distance between Q and Rajat = 7 9 km The distance between P and Rajat = PQ - RQ = 4 5 - 7 9 = 36 45 - 35 45 = 1 45 Hence, Rajat is 1 45 km away from point P and 7 9 km away from point Q.

Rashi earns ₹ 18,000 per month. She spends 1 4 of her income on groceries, 2 25 of the remainder on medicine, and 1 3 of the remainder on the education of children. How much money is still left with her?

Given, Rashi earns ₹ 18,000 per month She spends 1 4 of her income on groceries She spends 2 25 of remainder on medicine She spends 1 3 of remainder on education of children. We know that , Remaining fraction= 1 - Fraction spent Remaining income after groceries = 1 - 1 4 of total earning. = 3 4 × 18000 = ₹ 1350 0 Remainder income after medicine = 1 - 2 25 of remaining income after groceries. = 23 25 × 1 35 00 = ₹ 12420 Remainder income after education of children= 1 - 1 3 of remainder income after medicine. = 2 3 × 1 242 0 = ₹ 8280 So, the total money left is ₹ 8280 Therefore, the required answer is ₹ 8280

The product of two rational numbers is 18 35 . If one of them is - 8 7 , find the other.

Given, The product of two rational numbers is 18 35 . Let a = - 8 7 and b = ? Since, a × b = a b ∴ - 8 7 × b = 18 35 b = 18 35 × 7 - 8 b = - 9 20 Therefore, the required answer is - 9 20 .