The ratio of the present age of a man and his wife is 4 : 3 and 4 years hence, the ratio of their ages will be 9 : 7. If the ratio of their ages at the time of their marriage was 13 : 9, how many years ago were they married?

Solution
Person's age = 4x years
Wife's age = 3x years
After 4 years,\(\frac{4x+4}{3x+4}=\frac{9}{7}\)
⇒ 28x+ 28 = 27x+ 36
⇒ x=3628=8
∴ Person's age = 4 × 8 = 32 years
Wife's age = 3 × 8 = 24 years
If they got married y years ago, then\(\frac{32y}{24y}=\frac{13}{9}\)
⇒31213y=2889y
⇒ 13y9y=312288
⇒ 4y=24⇒y=6years
When 1 is added to \(\frac{13}{15}\) the part of \(\frac{7}{8}\) then it is equal to nth part of \(\frac{13}{7}\) Then n =

Solution
\(\frac{7}{8}\times \frac{13}{15}+1=\frac{91}{120}+1\)
\(=\frac{91+120}{120}=\frac{211}{120}\)
\(∴ \: \frac{211}{120}=\frac{13}{7n}\)
⇒ 7n×211 = 120×13
\(\Rightarrow \: n=\frac{120\times 13}{7\times 211 }=\frac{1560}{1477}\)
What is the least number which when increased by 13 is divisible by each of 42, 36 and 45?

Solution
Required number = LCM of 42, 36 and 45  13
∴ LCM = 2 × 3 × 3 × 7 × 2 × 5
= 1260
∴ Required number
= 1260 13 = 1247
Large Natural gas deposits have been recently discovered in the state of

Solution
Large Natural gas deposits have been recently discovered in the state of Rajasthan.
Muga variety of silk is native to the state of

Solution
Muga variety of the silk is the product of the silkworm Antheraea assamenis endemic to Assam.
The Stngalila National Park is located in the state of

Solution
The Singalila National Park is located on Singalila Ridge at an altitude of more than 7000 feet above sea level. in Darjeeling district of West Bengal.
Clement Attlee’s announcement proclaimed in the Parliament

Solution
The British Prime Minister, Clement Attlee on February 20, 1947 made the momentous declaration : "The present state of uncertainty is fraught with danger and cannot be indefinitely prolonged. His Majesty's overnment wish to make clear that it is their definite intention to take necessary steps to effect the transference of power to reponsible Indian hands by June 1948".
The MontagueChelmsford reform was passed in the year

Solution
The MontagueChelmsford reforms were passed in the year 1919. Main provisions of the Government of India Act, 1919:
(a) Number of Indians in GovernorGeneral's Executive Council was raised to three in a Council of eight.
(b) Dyarchy in provinces: The scheme necessitated demarcation of subject of administration between the Central and Provincial governments
(c) The Central Legislative Assembly was also enlarged by making it bicameral Council of States and the Legislative Council.
Lord William Bentinck was the governor general during the period

Solution
Lord Willlam Bentinck was the GovernorGeneral of India during 182835. Some of the
important works accomplished during his reign: Abolition of Sati (1829), Supresston
of Thug (1830).Codification of law by Macaulay etc
The system of payment of salary to the troops was decreed by

Solution
The system of payment of salary to the troops was decreed by Balban (12661287)