Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x     =>     x = ( 23 x 13/10 )     =>     x = 299 /10.

A's 1 day's work = 1/23 ;
B's 1 day's work = 10/299 .

(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 113 .

Therefore, A and B together can complete the work in 13 days. 

0.46 = 46/100 = 23/50.

Sum of the numerator and denominator is 23 + 50 = 73

The Indian Institute of Technology (IIT) Kharagpur has collaborated with the British Geological Survey (BGS) to turn Varanasi into a smart city. As part of the project, three dimensional geological modelling of the geology under Varanasi will be prepared to help improve the building of new transport and service infrastructure. The project includes application of geo-scientific methods like drilling, geological, geophysical, tectonics, hydrogeological and remote sensing. It would be the first major 3D subsurface urban study and planning of its kind in India, with the ultimate aim of developing methodologies and input of suburban geology for planning and hazard risk assessment. The purpose of the project is to develop the methodologies and approaches of urban geosciences and engineering of Varanasi as a pilot for other Indian cities.

Two times IPL champions Mumbai Indians (MI) reached a new milestone as they became the first team in history to win 100 T20 matches. The Mumbai outfit defeated Kolkata Knight Riders (KKR) at the Eden Gardens by 9 runs in their final match of the league stage of IPL 2017.

India’s first contactless business credit card has been launched by ICICI bank in association with Jet Airways, India premier international airline, for Small and Mid-sized Enterprises (SMEs) and their employees. The card has been christened as the ‘Jet Airways ICICI Bank Business Advantage Card’, which helps customers to save on their business expenses. The card is powered by the ‘VISA payWave’ contactless technology that enables the cardholder to make payments by simply tapping the card at contactless enabled terminals in more than 48 countries, including India. The card can also be used by dipping or swiping at non-contactless merchants.

The 112-feet tall bust of ‘Adiyogi’ Lord Shiva at the Isha Yoga Foundation has been declared the world’s largest bust by the Guinness Book of World Records. The Guinness had announced this on its website. The bust at the Isha Yoga Foundation on the outskirts of Coimbatore, Tamil Nadu was unveiled by Prime Minister Narendra Modi on 24 February.

Let P's speed = x km/hr. Then, Q's speed = (7 - x) km/ hr.

So, 24/x + 24/(7 - x) = 14

x2 - 98x + 168 = 0

(x - 3)(x - 4) = 0 => x = 3 or 4.

Since, P is faster than Q,

so P's speed = 4 km/hr and Q's speed = 3 km/hr.

Let the number be x. Then,

3x2 - 4x = x + 50

3x2- 5x - 50 = 0

(3x + 10)(x - 5) = 0

x = 5